Authors and papers citing work by Lee Rudolph

[Last updated May 4, 2008.]

Recent additions

In psychology, Paul van Geert has made some use of my proposed models of psychological time. He writes, ``Every now and then an image pops up that has the power to change the perspective on many other images. Lee Rudolph's (2006a) `the fullness of time' is such an image (for me, at least).''

In robotics, Anna Yershova and Steve La Valle ``show that efficient sampling-based motion planning'' for a mechanism with a closed chain ``is possible without having either'' a characterization of ``the geometry and topology of the closure set'' or a knowledge of the chain's inverse kinematics; but they do note that the ``new parametrization'' described in the topological, IK-focused paper Stratified configuration space and path planning for a planar closed chain with revolute joints [Han, Rudolph, Blumenthal & Valodzin 2006b] ``may lead to efficient motion planning algorithms in the future.'' We hope so!

In knot theory, Bae, Kim, and Park and Furihata, Hirasawa, and Kobayashi have made interesting applications of the special Seifert surfaces I named ``baskets''. Olga Plamenevskaya has proved that a new Khovanov-homological invariant is non-zero on quasipositive links. Sebastian Baader and Masaharu Ishikawa have given the negative answer to a question about braided surfaces that I asked in 1998. David Cimasoni and Matthew Hedden have proved new results on sliceness of various kinds of doubled knots. Hiroshi Goda has further developed circle-valued Morse theory for knots and links.

Elsewhere in low-dimensional topology, Jae Choon Cha has made progress on the minimal genus problem for topologically locally flat surfaces in 4-manifolds. Mikhail Khovanov and Richard Thomas are developing a theory of braid cobordisms using triangulated categories; they note that ``Braid cobordisms ... originally appeared in Rudolph [Ru]'', where I called them ``braided surfaces''. In 1983 I would never have guessed that triangulated categories would someday appear in association with braided surfaces -- though I did write, hopefully and innocently, that ``Perhaps some natural incidence structure, of the `building' sort, awaits discovery'' in the combinatorial infrastructure of a braided surface.

S. S. Abhyankar and A. Sathaye

[1996] Uniqueness of plane embeddings of special curves, Proc. Amer. Math. Soc. 124 (1996), 1061-1069. {Cites [Rudolph 1982].}

Selman Akbulut and Rostislav Matveyev

[1997] Exotic structures and adjunction inequality, Turkish Journal of Math. 21 (1997), 47-53. {Cites [Rudolph 1995b].}

Selman Akbulut and Burak Ozbagci

[2001] Lefschetz fibrations on compact Stein surfaces, Geometry and Topology 5 (2001), 319-334. {Cites [Rudolph 1992b, 1992c, 1995b, 1998].}

Gerald Allison, Avner Ash, and Eric Conrad

[1998] Galois representations, Hecke operators, and the mod-p cohomology of GL(3, Z) with twisted coefficients, Exp. Math. 7 (1998), 361-390. {Cites [Ash & Rudolph 1979].}

G. Aragon-Gonzalez, J. L. Aragon, and M. A. Rodriguez-Andrade

[2006] The decomposition of an orthogonal transformation as a product of reflections, J. Mathematical Physics 47 (2006), article number 013509. {Cites [Rudolph 1991].}

Enrique Artal Bartolo

[1995] Une démonstration géométrique du théorème d'Abhyankar-Moh, J. reine angew. Math. 464 (1995), 97-108. {Cites [Rudolph 1982].}

Avner Ash

[1980] Cohomology of congruence subgroups of SL(n, Z), Math. Ann. 249 (1980), 55-73.

[1983] On the top Betti number of subgroups of SL(n, Z), Math. Ann. 264 (1983), 277-281.

[1986] A note on minimal modular symbols, Proc. Amer. Math. Soc. 96 (1986), 394-396.

[1988] Non-minimal modular symbols for GL(n), Invent. Math. 91 (1988), 438-491.

[1989] Farrell cohomology of GL(n, Z), Israel J. Math. 67 (1989), 327-336.

[1994] Unstable cohomology of SL(n, O), J. Algebra 167 (1994), 330-342.

{All cite [Ash & Rudolph 1979].}

Avner Ash, Daniel Grayson, and Philip Green

[1984] Computations of cuspidal cohomology of congruence subgroups of SL(3; Z), J. Number Theory 19 (1984), 412-436. {Cites [Ash & Rudolph 1979].}

Avner Ash, Paul Gunnells, and Mark McConnell

[2002] Cohomology of congruence subgroups of SL(4, Z), J. Number Theory 94 (2002), 181-212. {Cites [Ash & Rudolph 1979].}

Avner Ash and Mark McConnell

[2002] Experimental indications of three-dimensional Galois representations from the cohomology of SL(3,Z), Experiment. Math. 1 (1992), 209-223. {Cites [Ash & Rudolph 1979].}

Tadashi Ashikaga and Hisaaki Endo

[2006] Various aspects of degenerate families of Riemann surfaces, Sugaku Expositions 19, 171-196. {Cites [Rudolph 1998].}

Abdallah Assi and Avinash Sathaye

[2005] On quasihomogeneous curves, preprint (2005). {Cites [Neumann & Rudolph 1987a].}

Ruth Auerbach

[1995] Loose-ended knots, preprint (1995). {Cites a lecture at the Mt. Holyoke College Research Experience for Undergraduates on algebraic singularities, 1995.}

Sebastian Baader

[2005a] Slice and Gordian numbers of track knots, Osaka J. Math. 42 (2005), 257-271. {Cites [Rudolph 1995b, 1999].}

[2005b] Quasipositivity and homogeneity, Math. Proc. Camb. Phil. Soc. 139 (2005), 287-290. {Cites [Rudolph 1983bd, 1998, 1999].}

[2005c] Notes on quasipositivity and combinatorial knot invariants, Ph.D. thesis, University of Basel (2004). {Cites [Rudolph 1983bd, 1992c, 1993, 1998, 1999 2005].}

[2006a] Construction of non-alternating knots, Proc. Amer. Math. Soc., published electronically March 14, 2007 (preprint, 2006). {Cites [Rudolph 1995b].}

[2006b] Moebius bands with a quasipositive fibred hole, preprint (2006). {Cites [Rudolph 1983bd, 1999].}

[2006c] Vassiliev invariants of quasipositive knots, Compositio Mathematica 142 (2006), 1343-1350. {Cites [Rudolph 1983bd].}

[2007] Asymptotic Rasmussen Invariant, Comptes Rendus Math. 345, 225-228. {Cites [Rudolph 1993].}

[2008] Asymptotic link invariants for ergodic vector fields, preprint (2008). {Cites [Rudolph 1993].}

Sebastian Baader, Kai Cieliebak, and Thomas Vogel

[2007] Legendrian ribbons in overtwisted contact structures, preprint (2007). {Cites [Rudolph 1992c.]}

Sebastian Baader and Masaharu Ishikawa

[2006] Legendrian graphs and quasipositive diagrams, preprint (2006). {Cites [Rudolph 1995b, 1999].}

Yongju Bae, Dongseok Kim, and Chan-Young Park

[2006] Basket, flat plumbing and flat plumbing basket numbers of links, preprint (2006). {Cites [Rudolph 1983e, 1988a, 1992b, 1998, 2001b]

Kenneth Baker

[2004] Knots on once-punctured torus fibers, Ph.D. thesis, University of Texas (2004). {Cites [Rudolph 2001b].}

Riccardo Benedetti and Masahiro Shiota

[1998] On real algebraic links in S³, Boll. Unione Mat. Italiana 3 (1998), 585-609. {Cites [Rudolph 1987b].}

D. Bennequin

[1983] Entrelacements et équations de Pfaff, Astérisque 107-108 (1983), 87-161. {Cites [Rudolph 1983de].}

[1990] Topologie Symplectique, convexité holomorphe et structures de contact [d'après Y. Eliashberg, D. Mc Duff et al.], Astérisque 189-90 (1990), 85-323. {Cites [Rudolph 1984a].}

Joan Birman and Ilya Kofman

[2007] Lorenz knots, T-links and twisted torus links, preprint (2007).

J. Birman, P. Boldi, M. Rampichini, and S. Vigna

[2002] Towards an implementation of the B-H algorithm for recognizing the unknot, J. Knot Theory Ramif. 11 (2002), 601-646. {Cites [Rudolph 1998].}

J. Birman, K. H. Ko, and S. J. Lee

[1998] A new approach to the word and conjugacy problems in the braid groups, Adv. Math. 139 (1998), 322-353. {Cites [Rudolph 1983e].}

J. S. Birman and W. W. Menasco

[1991] Studying links via closed braids (2): On a theorem of Bennequin, Topol. Appl. 40 (1991), 71-82. {Cites [Rudolph 1985b.]}

[1992a] Studying links via closed braids (1): A finiteness theorem, Pac. J. Math. 154 (1992), 17-36. {Cites [Rudolph 1985b].}

[1992b] Studying links via closed braids (5): The unlink, Trans. Amer. Math. Soc. 329 (1992), 585-606. {Cites [Rudolph 1983e].}

[1993] Studying links via closed braids (3): Classifying links which are closed 3-braids, Pac. J. Math. 161 (1993), 25-113. {Cites [Rudolph 1983e].}

J. Birman and R. F. Williams

[1983] Knotted periodic orbits in dynamical systems. I. Lorenz's equations, Topology 22 (1983), 47-82. {Cites [Rudolph 1983c].}

Zarko Bizaca

[1995] An explicit family of exotic Casson handles, Proc. Amer. Math. Soc. 123 (1995) 1297-1302. {Cites [Rudolph 1993].}

Zarko Bizaca and Robert Gompf

[1996] Elliptic surfaces and some simple exotic R⁴s, J. Differ. Geom. 43 (1996), 458-504. {Cites [Rudolph 1993].}

Arnaud Bodin

[1999] Milnor fibration and fibered links at infinity, International Mathematics Research Notices 11 (1999), 615-622. {Cites [Neumann & Rudolph 1987a].}

[2000] Fibres et entrelacs irréguliers à l'infini, doctoral thesis, Université Paul Sabatier, Toulouse (2000). {Cites [Neumann & Rudolph 1987a], [Rudolph 1982].}

[2002a] Classification of polynomials from C² to C with one critical value, Mathematische Zeitschrift 242 (2002), 303-322. {Cites [Neumann & Rudolph 1987a], [Rudolph 1982].}

[2002b] Non reality and non connectivity of complex polynomials, C. R. Math. 335 (2002), 1039-1042. {Cites private communication, 1998.}

[2008] Integral points on generic fibers, preprint (2008). {Cites [Neumann & Rudolph 1987a], [Rudolph 1982].}

Arnaud Bodin and Anne Pichon

[2007] Meromorphic functions, bifurcation sets and fibred links, Math. Res. Lett. 14 (2007), 413-422. {Cites [Hirasawa & Rudolph 2007].}

Christian Bohr

[2002] On the kinkiness of closed braids, J. Knot Theory Ramif. 11 (2002), 1155-1163. {Cites [Rudolph 1983d, 1993, 1999].}

Christian Bohr and Ronnie Lee

[2002] Homology cobordism and classical knot invariants, Comment. Math. Helv. 77 (2002), 363-382. {Cites [Rudolph 1993].}

Michel Boileau and Laurence Fourrier

[1998] Knot theory and plane algebraic curves, Chaos Solitons Fractals 9 (1998), 779-792. {Cites [Boileau & Rudolph 1995a], [Neumann & Rudolph 1987a], [Rudolph 1982, 1983bde, 1984b, 1985b, 1990b, 1992bc, 1995b, 1998].}

Michel Boileau and Stepan Yu. Orevkov

[2001] Quasipositivité d'une courbe analytique dans une boule pseudo-convexe, C. R. Acad. Sci. Paris 332 (2001), 825-830. {Cites [Boileau & Rudolph 1995a], [Rudolph 1983a].}

Michel Boileau and Claude Weber

[1983] Le problème de J. Milnor sur le nombre gordien des noeuds algébriques, Noeuds, Tresses, et Singularités (Plans-sur-Bex, 1982), 49-98, Monogr. Enseign. Math., 31, Enseignement Math., Geneva, 1983. {Cites [Rudolph 1983e].}

Maciej Borodzik and Henryk Zoladek

[2007a] Complex-algebraic plane curves via the Poincaré-Hopf formula, I. Parametric lines, Pacific J. Math. 229, 307-338. {Cites [Rudolph 1982, 1983a].}

[2007b] Complex-algebraic plane curves via the Poincaré-Hopf formula, II. Annuli, preprint (2007). {Cites [Rudolph 1983a], [Neumann & Rudolph 1987a].}

Thomas Brélivet

[2002] Topologie des polynômes, spectre et variance du spectre, doctoral thesis, Uni. Bordeaux, 2002.

[2005] Sur les paires spectrale de polynômes à deux variables, Actes du Colloque ``Singularitées franco-japonaises'', Séminaires & Congrès 10, Soc. Math. France, 2005, pp. 39-59.

{Both cite [Neumann & Rudolph 1987a].}

Nathan Broaddus

[2007] Homology of the curve complex and the Steinberg module of the mapping class group, preprint (2007). {Cites [Ash & Rudolph 1979].}

J. W. Bruce and T. J. Gaffney

[1982] Simple singularities of mappings C,0 -> C²,0, J. London Math. Soc. 26 (1982), 465-474. {Cites [Rudolph 1976a].}

Gerhard Burde and Heiner Zieschang‌†

[2003] Knots (second edition), de Gruyter Studies in Mathematics 5. Walter de Gruyter & Co., Berlin, 2003. {Cites [Pajitnov, Rudolph & Weber 2002], [Rudolph 1982, 1985b, 1987b, 1993, 1998].}

V. A. Bykovskii

[2003] Generating Elements of the Annihilating Ideal for Modular Symbols, Functional Analysis and Its Applications 37 (2003), 263-272. {Cites [Ash & Rudolph 1979].}

Melvin G. Calkin

[1996] Lagrangian And Hamiltonian Mechanics, World Scientific Publishing Co. (1996). {Cites [Abelson, di Sessa, & Rudolph 1975].}

Vera Carrara, J. Scott Carter, and Masahico Saito

[2001] Singularities of the projections of surfaces in 4-space, Pacific J. Math. 199 (2001), 21-40. {Cites [Rudolph 1983e].}

J. Scott Carter, Daniel Jelsovsky, Seiichi Kamada, Laurel Langford, and Masahico Saito

[1999] State-sum invariants of knotted curves and surfaces from quandle cohomology, Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 146-156.

[2003] Quandle cohomology and state-sum invariants of knotted curves and surfaces, Trans. Amer. Math. Soc., 2003.

{Both cite [Rudolph 1983e].}

J. Scott Carter, Daniel Jelsovsky, Seiichi Kamada, and Masahico Saito

[2001] Computations of quandle cocycle invariants of knotted curves and surfaces, Adv. Math. 157 (2001), 36-94. {Cites [Rudolph 1983e].}

J. Scott Carter, Seiichi Kamada, and Masahico Saito

[2000] Alexander numbering of knotted surface diagrams, Proc. Amer. Math. Soc. 128 (2000), 3761-3771. {Cites [Rudolph 1983e].}

J. Scott Carter and Masahico Saito

[1995] Knot diagrams and braid theories in dimension 4, in Real and complex singularities (Sao Carlos, 1994), Pitman Res. Notes Math. Ser., 333, Longman, Harlow, 1995, pp. 112-147.

[1996] Braids and movies, J. Knot Theory Ramif. 5 (1996), 589-608.

{Both cite [Rudolph 1983e].}

Pierette Cassou-Nogues

[1996] Sur la généralisation d'un théorème de Kouchnirenko, Compos. Math. 103 (1996), 95-121. {Cites [Neumann & Rudolph 1987a].}

John Casti

[2000] Five more golden rules: knots, codes, chaos, and other great theories of 20th-century mathematics, John Wiley & Sons, 2000. {Cites [Menasco & Rudolph 1995c].}

Miran Cerne

[2000] Analytic discs attached from the outside have knotted boundaries, Bull. London Math. Soc. 32 (2000), 339-344. {Cites [Rudolph 1983e.}

Jae Choon Cha

[2006] Topological minimal genus and L²-signatures, preprint (2006). {Cites [Rudolph 1995b, 1997.]}

Hai-Chau Chang and Lih-Chung Wang

[1993] An intersection theoretical proof of the embedding line theorem, J. Algebra 161 (1993), 467-479. {Cites [Rudolph 1982].}

Gautam Chinta, Paul Gunnells, and Robert Sczech

[2000] Computing special values of partial zeta functions, Algorithmic number theory (Leiden, 2000), Lecture Notes in Comput. Sci. 1838, Springer, Berlin, 2000. {Cites [Ash & Rudolph 1979].}

S. Chmutov and V. Goryunov

[1997] Polynomial invariants of Legendrian links and plane fronts, in Topics in singularity theory, Amer. Math. Soc. Transl. Ser. 2, 180 (1997), pp. 25-43. {Cites [Rudolph 1990b].}

David Cimasoni

[2002] Alexander invariants of multilinks, Ph.D. thesis, University of Geneva. {Cites [Neumann & Rudolph 1987a, 1990a].}

[2004a] The Conway potential function of a graph link, Math. Proc. Camb. Phil. Soc. 136 (2004), 557-563. {Cites [Neumann & Rudolph 1987a].}

[2004b] The Alexander module of links at infinity, Int. Math. Res. Not. 2004 20 (2004), 1023-1036. {Cites [Neumann & Rudolph 1987a].}

[2006] Slicing Bing doubles, Algebraic and Geometric Topology 6 (2006), 2395-2415. {Cites [Rudolph 1993, 1995b].}

Calvin C. Clawson

[1999] Mathematical Mysteries: The Beauty and Magic of Numbers, Da Capo Press, 1999.

John Clement and Jack Lochhead

[1979] Cognitive Process Instruction: Research on Teaching Thinking Skills, Franklin Institute Press, 1979. {Cites [Abelson, di Sessa, & Rudolph 1975].}

Tim Cochran and Robert Gompf

[1988] Applications of Donaldson theorems to classical knot concordance, homology 3-spheres and Property-P, Topology 27 (1988), 495-512. {Cites [Rudolph 1983c].}

Peter R. Cromwell

[2004] Knots and links, Cambridge University Press, Cambridge, 2004. {Cites [Rudolph 1992b.]}

Daniel C. Cohen and Alexandru I. Suciu

[1997] The braid monodromy of plane algebraic curves and hyperplane arrangements, Comment. Math. Helv. 72 (1997), 285-315. {Cites [Rudolph 1983a].}

P. Cointe

[1984] Une extension de VLISP vers les objets, Science of Computer Programming 4 (1984), 291-322. {Cites [Abelson, Goodman & Rudolph 1974].}

F. Curado and J. F. Valente

[1978] Some problems of translating LOGO to a romance language, ACM SIGCUE Outlook 12 (1978), 11-29. {Cites [Abelson, Goodman & Rudolph 1974].}

Oliver T. Dasbach and Brian S. Mangum

[2001] On McMullen's and other inequalities for the Thurston norm of link complements, Algebraic and Geometric Topology 1 (2001), 321-347. {Cites [Rudolph 1993, 1999].}

David Derbes

[2001] Reinventing the wheel: Hodographic solutions to the Kepler problems, Am. J. Physics 69 (2001), 481-489. {Cites [Abelson, di Sessa, & Rudolph 1975].}

Yuanan Diao, Claus Ernst, and Andrzej Stasiak

[2006] A partial ordering of knots through diagrammatic unknotting, preprint (2006). {Cites [Rudolph 1993.]}

Alexandru Dimca

[1998] Monodromy at infinity for polynomials in two variables, J. Algebraic Geom. 7 (1998), 771-779. {Cites [Neumann & Rudolph 1987a].}

Alexandru Dimca and András Némethi

[2004] Hypersurface complements, Alexander modules and monodromy, Proceedings of the Conference: Real and Complex Singularities, San Carlos, Brazil, August 2002, Contemporary Mathematics 354 (2004), 19-43. {Cites [Neumann & Rudolph 1987a].}

Rainer Diriwaechter

[2006] The wandering soul in relation to time, Culture & Psychology 12 (2006), 161-167. {Cites [Rudolph 2006c].}

Andrea A. di Sessa

[1980] Computation as a physical and intellectual environment for learning physics, Computers and Education 4 (1980), 67-75. {Cites [Abelson, di Sessa, & Rudolph 1975].}

Simon K. Donaldson

[1988] Complex curves and surgery, Inst. Hautes Études Sci. Publ. Math. No. 68 (1988), 91-97. {Cites [Rudolph 1984a].}

J. F. Dumais

[1979] Geometry of the Kepler initial-value problem explored with 2 circles, Am. J. Physics 47 (1979), 519-524. {Cites [Abelson, di Sessa, & Rudolph 1975].}

Nathan M. Dunfield, Sergei Gukov, and Jacob Rasmussen

[2005] The superpolynomial for knot homologies, Experimental Mathematics 14 (2005). {Cites [Rudolph 1995b, 1999].}

Alan H. Durfee and Donal O'Shea

[2006] Polynomial knots, preprint (2006). {Cites a lecture at the Mt. Holyoke College Research Experience for Undergraduates on algebraic singularities, 1995.} [Rudolph 1982].}

Alan H. Durfee

[1999] Singularities, in History of Topology, ed. I. M. James, North-Holland, Amsterdam (1999), 417-434. {Cites [Rudolph 1982].}

Ehtibar N. Dzhafarov

[2006] Mathematical theorizing versus mathematical metaphorizing: A commentary on Rudolph, Culture & Psychology 12 (2006), 205-214. {Cites [Rudolph 2006c].}

David Eisenbud and Walter Neumann

[1986] Three-Dimensional Link Theory and Invariants of Plane Curve Singularities, Annals of Mathematics Studies 110. {Indirectly cites [Rudolph 1976b].

Eaman Eftekhary

[2005] Longitude Floer homology and the Whitehead double, Algebraic & Geometric Topology 5 (2005), 1389-1418. {Cites [Rudolph 1997.]}

T. Ekholm, J. Etnyre, and M. Sullivan

[2005] Legendrian submanifolds in R²ⁿ⁺¹ and contact homology, preprint (2002). {Cites [Rudolph 1995b].}

Yakov Eliashberg and Maia Fraser

[1998] Classification of topologically trivial Legendrian knots, in Geometry, topology, and dynamics (Montreal, PQ, 1995), CRM Proc. Lecture Notes 15, Amer. Math. Soc., Providence, RI, 1998, pp. 17-51. {Cites [Rudolph 1995d].}

[2008] Topologically trivial Legendrian knots, preprint (2008). {Cites [Rudolph 1990b, 1995d].}

Judith Epstein and Dmitry Fuchs

[2001] On the invariants of Legendrian mirror torus links, in Symplectic and contact topology: interactions and perspectives (Toronto, ON/Montreal, QC, 2001), pp. 103-115. {Cites [Rudolph 1993].}

Arno van den Essen

[1995] Seven lectures on polynomial automorphisms, in Automorphisms of affine spaces (Curacao, 1994) Kluwer Acad. Publ., Dordrecht, 1995, pp. 3-39.

[1997] Polynomial automorphisms and the Jacobian conjecture, in Algèbre non commutative, groupes quantiques et invariants (Reims, 1995), Soc. Math. France, 1997, 55-81.

[2003] Around the Abhyankar-Moh Theorem, in Algebra, Arithmetic, and Geometry, With Applications: Papers from Shreeram S. Abhyankar's 70th Birthday Conference, Springer, 2003, pp. 283-294.

{All cite [Rudolph 1982].}

John B. Etnyre

[1998] Symplectic convexity in low-dimensional topology, Topol. Appl. 88 (1998), 3-25. {Cites [Rudolph 1995b].}

[1999] Transversal torus knots, Geometry and Topology 3 (1998), 253-268. {Cites [Rudolph 1995b].}

[2000] Tight contact structures on lens spaces, Commun. Contemp. Math. 2 (2000), 559-577; corrigendum. {Cites [Rudolph 1995b].}

[2005] Legendrian and transversal knots, in Handbook of Knot Theory (William Menasco and Morwen Thistlethwaite, eds.), Elsevier (2005). {Cites [Rudolph 1990b, 1995b].}

John B. Etnyre and Robert Ghrist

[2002] Tight contact structures and Anosov flows, Topology and its Applications 124 (2002), 211-219. {Cites [Rudolph 1995b].}

John B. Etnyre and Ko Honda

[2001a] Knots and contact geometry I: Torus knots and the figure eight knot, J. Symplectic Topology 1 (2001), 63-120.

[2001b] On the non-existence of tight contact structures, Annals of Math. 153 (2001), 749-766.

{Both cite [Rudolph 1995b].}

John B. Etnyre and Lenhard L. Ng

[2003] Problems in low-dimensional contact topology, Topology and Geometry of Manifolds (Proceedings of the 2001 Georgia International Topology Conference), Proc. Sympos. Pure Math. 71 (2003), 337--357. {Cites [Rudolph 1995b].}

John B. Etnyre, Lenhard L. Ng, and Joshua M. Sabloff

[2002] Invariants of Legendrian knots and coherent orientations, J. Symplectic Geom. 1 (2002), 321-367. {Cites [Rudolph 1995b].}

John B. Etnyre and Burak Ozbagci

[2008] Invariants of contact structures from open books, Trans. Amer. Math. Soc. 360 (2008), 3133-3151 (preprint, 2006). {Cites [Neumann & Rudolph 1990a].}

Emmanuel Ferrand

[1999] On Legendre cobordisms, Differential and symplectic topology of knots and curves, ed. S. Tabachnikov, Advances in the Mathematical Sciences 42 (1999), 23-35. {Cites [Rudolph 1990b, 1992b, 1993, 1995b].}

[2002] On Legendrian knots and polynomial invariants, Proc. Amer. Math. Soc. 130 (2002), 1169-1176. {Cites [Rudolph 1984b, 1990b, 1992ab, 1993, 1995b].}

[2005] Topologie et combinatoire des sous-variétés legendriennes, habilitation, 2005. {Cites [Rudolph 1984b, 1990b, 1992ab, 1993, 1995b].}

Thomas Fiedler

[1989] Complex-plane curves in the ball, Invent. Math. 95 (1989), 479-506. {Cites [Rudolph 1983ab].}

[1991a] On the degree of the Jones polynomial, Topology 30 (1991), 1-8. {Cites [Rudolph 1983e].}

[1991b] Algebraic links and the Hopf fibration, Topology 30 (1991), 259-265. {Cites [Rudolph 1983a].}

[1993] A small state sum for knots, Topology 32 (1993), 281-294. {Cites [Rudolph 1983e].}

[2001] Gauss diagram invariants for knots and links, Springer, 2001. {Cites [Rudolph 1983d].}

Vincent Florens

[2005] Signatures of colored links with application to real algebraic links, J. Knot Theory Ramif. 14 (2005), 883-918. {Cites [Rudolph 1997].}

Laurence Fourrier

[1994] Topological classification at infinity of polynomials of 2 complex variables, C. R. Acad. Sci. Paris 318 (1994), 461-466.

[1996] Topological types of polynomials of two complex variables at infinity, Ann. Inst. Fourier 46 (1996), 645-687.

{Both cite [Neumann & Rudolph 1987a], [Rudolph 1982].}

John Franks and R. F. Williams

[1987] Braids and the Jones polynomial, Trans. Amer. Math. Soc. 303 (1987), 97-108. {Cites [Rudolph 1983e].}

Dmitry Fuchs and Serge Tabachnikov

[1997] Invariants of Legendrian and transverse knots in the standard contact space, Topology 36 (1997), 1025-1053. {Cites [Rudolph 1990b].}

Rei Furihata, Mikami Hirasawa, and Tsuyoshi Kobayashi

[2005] Seifert surfaces in open books, and a new coding algorithm for links, preprint (2005). {Cites [Rudolph 2001b].}

Martin Gardner

[1997] Last Recreations: Hydras, Eggs, and other Mathematical Mystifications, Springer Verlag, 1997.

[2001] The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems, W. W. Norton & Company, 2001.

{Both cite [Menasco & Rudolph 1995c].}

Bert van Geemen, Wilberd van der Kallen, Jaap Top, and Alain Verberkmoes

[1997] Hecke eigenforms in the cohomology of congruence subgroups of SL(3,Z), Experimental Mathematics 6 (1997), 163-174. {Cites [Ash & Rudolph 1979].}

Bert van Geemen and Jaap Top

[2000] Modular forms for GL(3) and Galois representations, Lect. Notes Comput. Sci. 1838 (2000), 333-346. {Cites [Ash & Rudolph 1979].}

William Gibson

[2002] Oriented divides and plane curve braids, J. Knot Theory Ramif. 11 (2002), 973-1016. {Cites [Rudolph 1983d].}

Emmanuel Giroux

[2003] Géométrie de contact: de la dimension trois vers les dimensions supérieures, Proceedings of the International Congress of Mathematicians, Beijing 2002, Volume 3, 405-414. {Cites [Neumann & Rudolph 1987a].}

Emmanuel Giroux and Noah Goodman

[2006] On the stable equivalence of open books in three-manifolds, Geometry & Topology 10 (2006), 97-114. {Cites [Neumann & Rudolph 1987a, 1988b].}

Hiroshi Goda

[2006] Circle valued Morse theory for knots and links, in Floer Homology, Gauge Theory, and Low-Dimensional Topology (David A. Ellwood, Peter S. Ozsvath, Andras Stipsicz, and Zoltan Szabo, eds.), Clay Mathematics Proceedings, vol. 6, 2006, pp. 71-99. {Cites [Pajitnov, Rudolph, & Weber 2001a], [Hirasawa & Rudolph 2007], [Rudolph 2005].}

[2007] Some estimates of the Morse-Novikov numbers for knots and links, in Intelligence of Low Dimensional Topology 2006 (J. Scott Carter, editor), World Scientific, 2007, pp. 35-42. {Cites [Pajitnov, Rudolph, & Weber 2001a], [Hirasawa & Rudolph 2007], [Rudolph 2005].}

Hiroshi Goda and Andrei Pajitnov

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Hermann Gruber

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[1999] Modular symbols for Q-rank one groups and Voronoi reduction, J. Number Theory 75 (1999) 198-219.

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{All cite [Ash & Rudolph 1979].}

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[2001b] Links of plane curves, fiberedness, quasipositivity and Jones polynomials, doctoral thesis, Uni. Basel (2001). {Cites [Rudolph 1983d, 1995b, 1998].}

[2005] On the Thurston-Bennequin invariant of graph divide links, Math. Proc. Camb. Phil. Soc. 139 (2005), 487-495. {Cites [Rudolph 1995b].}

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Shulim Kaliman

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Tamás Kálmán

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{Both cite [Rudolph 1990b].}

Seiichi Kamada

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[1994b] Alexander and Markov theorems in dimension-4, Bull. Amer. Math. Soc. 31 (1994), 64-67. {Cites [Rudolph 1983e, 1985b.]}

[1996a] On braid monodromies of non-simple braided surfaces, Math. Proc. Camb. Phil. Soc. 120 (1996), 237-245. {Cites [Rudolph 1983de, 1984a, 1985b, 1992c, 1993.]}

[1996b] An observation of surface braids via chart description, J. Knot Theor. Ramif. 5 (1996), 517-529. {Cites [Rudolph 1983de, 1984a, 1985b.]}

[1996c] Crossing changes for singular 2-dimensional braids without branch points, Kobe J. Math. 13 (1996), 177-182.

[1996b] Surfaces in 4-space: a view of normal forms and braidings, in Lectures at Knots '96 (Shin'ichi Suzuki, editor), World Scientific (1996), pp. 39-71. {Cites [Rudolph 1983de, 1984a, 1985b].}

[1998] Standard forms of 3-braid 2-knots and their Alexander polynomials, Mich. Math. J. 45 (1998), 189-205. {Cites [Rudolph 1983e, 1985b.]}

[1999a] Unknotting immersed surface-links and singular 2-dimensional braids by 1-handle surgeries, Osaka J. Math. 36 (1999), 33-49. {Cites [Rudolph 1983e, 1985b.]}

[1999b] Arrangement of Markov moves for 2-dimensional braids, Contemp. Math. 233 (1999), 197-213.

[2002] Braid and Knot Theory in Dimension Four (Mathematical Surveys and Monographs 95), American Mathematical Society (Providence), 2002. {Cites [Neumann & Rudolph 1987a], [Rudolph 1983bcde, 1984b, 1985b, 1986, 1987b, 1988a, 1990b, 1992abc.]}

[2007] Graphic descriptions of monodromy representations, Topol. Applic. (to appear, 2007). {Cites [Rudolph 1983e, 1985b.]}

Seiichi Kamada and Yukio Matsumoto

[2005] Enveloping monoidal quandles, Topology and its Applications 146-147 (2005), 133-148. {Cites [Rudolph 1983e, 1985b].}

Seiichi Kamada, Shin Satoh, and Manabu Takabayashi

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Tomomi Kawamura

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[2000] Lower bounds for the unknotting numbers of the knots obtained from certain links, in Knots in Hellas '98: Proceedings of the International Conference on Knot Theory and Its Ramifications, World Sci. Publ., Singapore (2000), 203-207. {Cites [Rudolph 1993].}

[2001] On unknotting numbers and four-dimensional clasp numbers of links, Proc. Amer. Math. Soc. 130 (2002), 243-252. {Cites [Rudolph 1983d, 1993, 1998, 1999].}

[2002a] Four-dimensional invariants of links and the adjunction formula, J. Knot Theory Ramif. 11, Special Issue: Knots 2000 Korea, Volume 1 (2002), 323-340. {Cites [Rudolph 1993, 1999].}

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[2004] Links associated with generic immersions of graphs, Algebraic and Geometric Topology 4 (2004), 571-594. {Cites [Rudolph 1983d, 1992a, 1993.]}

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[2006] Essential cycles in graph divides as a link representation, Tokyo J. Math. 29 (2006), 515-527. {Cites [Rudolph 1983d, 1992a, 1998].}

[2007] The Rasmussen invariants and the sharper slice-Bennequin inequality on knots, Topology 46 (2007), 29-38 (preprint, May 13, 2005; published online, November 28, 2006). {Cites [Rudolph 1993, 1999].}

Keiko Kawamuro

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[2006] The algebraic crossing number and the braid index of knots and links, Algebraic & Geometric Topology 6 (2006) 2313-2350. {Both cite Neumann & Rudolph 1990a].}

Akio Kawauchi

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[2007] A knot model in psychology (preprint, 2007).

Nicholas Kerr

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V. M. Kharlamov and V. S. Kulikov

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Mikhail Khovanov and Richard Thomas

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P. Kirk and C. Livingston

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K. H. Ko and S. J. Lee

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A. B. Korchagin and G. M. Polotovskii

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Dieter Kotschick and Gordana Matic

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Hanspeter Kraft

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Peter Kronheimer and Tomasz Mrowka

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Nathaniel Kuhn

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Ravindra S. Kulkarni and John W. Wood

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Ronnie Lee and Joachim Schwermer

[1986] Geometry and arithmetic cycles attached to SL₃(Z), Topology 25 (1986), 159-174. {Cites [Ash & Rudolph 1979].}

Ronnie Lee and Dariusz Wilczynski

[1997] Representing homology classes by locally flat surfaces of minimum genus, Am. J. Math. 119 (1997), 1119-1137. {Cites [Rudolph 1984a, 1993].}

Anatoly Libgober

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