Mathematical Publications of Lee Rudolph

[Last updated May 1, 2008]

[2008b] The Finite-Dimensional Freeman Thesis.

· Integrative Psychological and Behavioral Science, 42(2), 2008.

[2008a] Convexly Stratified Deformation Spaces and Efficient Path Planning for Planar Closed Chains with Revolute Joints (with Li Han, Jonathon Blumenthal, and Ihar Valodzin).

· Under review by International Journal of Robotics Research.

[2007a] A unified geometric approach to inverse kinematics of a spatial chain with spherical joints (with Li Han).

· To appear in Proceedings of ICRA 2007 (IEEE International Conference on Robotics and Automation, 2007).

[2007b] Constructions of Morse maps for knots and links, and upper bounds on the Morse-Novikov number (with Mikami Hirasawa).

· To appear in Journal of Knot Theory and its Ramifications, 2008.

· Illustrations.

· Cited in [Bodin & Pichon 2007], [Goda 2006, 2007], [Goda & Pajitnov 2005].

[2006a] Inverse kinematics for a serial chain with joints under distance constraints (with Li Han).

· Robotics: Science and Systems II (Gaurav Suhas Sukhatme, ed.), MIT Press (Cambridge, Mass.), 2007, pp. 177-184.

[2006b] Stratified configuration space and path planning for a planar closed chain with revolute joints (with Li Han, Jonathon Blumenthal, and Ihar Valodzin).

· To appear in Proceedings of WAFR 2006 (Seventh International Workshop on the Algorithmic Foundations of Robotics), Springer-Verlag, 2006.

· Cited in [Yershova & Lavalle 2006].

[2006c] The Fullness of Time, Culture and Psychology (volume 12, number 2), 157-186, 2006.

· Cited in [Diriwaechter 2006], [Dzhafarov 2006], [Hood 2006], [Muller & Giesbrecht 2006], [Thorngate 2006], [Valsiner 2006], [van Geert 2006], [Yamada & Kato 2006].

[2006d] Mathematics, Models and Metaphors, Culture and Psychology (volume 12, number 2), 245-265, 2006.

· Cited in [Valsiner 2005, 2006], [van Geert 2006].

[2006e] Spaces of Ambivalence: Qualitative Mathematics in the Modeling of Complex Fluid Phenomena, Estudios de Psicología (volume 27, number 1), 67-83, 2006.

· Cited in [Valsiner 2005, 2006].

[2005] Knot theory of complex plane curves. Chapter 8 of the Handbook of Knot Theory, edited by William Menasco and Morwen Thistlethwaite, Elsevier (2005), pp. 349-427.

· Cited in [Goda 2006, 2007], [Hedden & Ording 2005].

[2002a] Some fibered and non-fibered links at infinity of hyperbolic complex line arrangements.

· Topology and its Applications [special issue devoted to proceedings of Arrangements in Boston], 118 (2002), 187-197.

· Illustrations.

[2002b] A non-ribbon plumbing of fibered ribbon knots.

· Proceedings of the American Mathematical Society 130 (2002), 3741-3743.

· Publisher's on-line version (abstract available to all comers, full text to AMS subscribers only).

· Review (from Zentralblatt).

· Illustration.

[2002c] Isolated critical points of maps R⁴ to R², contact forms on S³, the enhanced Milnor number, and quasipositive fibered links.

· Abstract.

[2001a] The Morse-Novikov number for knots and links (with A. Pajitnov and C. Weber).

· Algebra i Analiz 13 (2001), 105-118; translation in St. Petersburg Math. J. 13 (2002), 417-426.

· Cited in [Burde & Zieschang 2003], [Goda 2006, 2007], [Goda & Pajitnov 2005], [Pajitnov 2004].

[2001b] Hopf plumbing, baskets, arborescent Seifert surfaces, espaliers, and homogeneous braids.

· Topology and its Applications 116 (2001), 255-277.

· Review (from Zentralblatt).

· Illustrations.

· Cited in [Bae, Kim, & Park 2006], [Baker 2004], [Furihata, Hirasawa, & Kobayashi 2006], [Kim & Lee 2007].

[2001c] Quasipositive pretzels.

· Topology and its Applications 115 (2001), 115-123.

· Publisher's on-line version (Elsevier subscribers only).

· Review (from Zentralblatt).

· Cited in [Livingston 2005a], [Nakamura 2004, 2007], [Stoimenow 2004a].

[2001d] Murasugi sums of Morse maps to the circle, Morse-Novikov numbers, and free genus of knots. (Subsumed into [Hirasawa & Rudolph 2003].)

· Illustrations.

[1999] Positive links are strongly quasipositive.

· Geometry and Topology Monographs 2 [Proceedings of the Kirbyfest] (1999), 555-562.

· Review (from Zentralblatt).

· Cited in [Baader 2005ab, 2006b], [Baader & Ishikawa 2006], [Bohr 2002], [Dasbach & Mangum 2001], [Dunfield, Gukov & Rasmussen 2005], [Hedden 2005], [Hirasawa 2001], [Hirasawa & Stoimenow 2003], [Kawamura 2001a, 2002ac, 2007], [Murasugi & Stoimenow 2003], [Nakamura 2000], [Przytycki 1997], [Rasmussen 2004, 2005], [Stoimenow 2000c, 2001ab, 2002d, 2003bd, 2004ab, 2005, 2006ad].

[1998] Quasipositive plumbing (Constructions of quasipositive knots and links, V).

· Proceedings of the American Mathematical Society 126 (1998), 257-267.

· Review (from Zentralblatt).

· Illustrations.

· Cited in [Akbulut & Ozbagci 2001], [Ashikaga & Endo 2006], [Baader 2005bc], [Bae, Kim, & Park 2006], [Birman, Boldi, Rampichini, & Vigna 2002], [Boileau & Fourrier 1998], [Burde & Zieschang 2003], [Hedden 2005], [Ishikawa 2001b], [Kawamura 2001a, 2006], [Rampichini 2004], [Tanaka 1998b].

[1997] The slice genus and the Thurston-Bennequin invariant of a knot.

· Proceedings of the American Mathematical Society 125 (1997), 3049-3050.

· Cited in [Cha 2006], [Eftekhary 2005], [Florens 2005], [Lisca & Stipsicz 2004], [Livingston 2005a], [Plamenevskaya 2004], [Tanaka 1999b, 2006], [Traynor 1998], [Wu 2005].

[1995a] Noeuds non concordants à un C-bord (with Michel Boileau).

· Vietnam Journal of Mathematics 23 [special issue constituting proceedings of the Seminaire Franco-Vietnamien sur l'analyse pluricomplexe et la topologie des singularités, Dalat, Vietnam, 1994] (1995), 13-28.

· Cited in [Boileau & Fourrier 1998], [Boileau & Orevkov 2001], [Kirby 1997].

[1995b] An obstruction to sliceness via contact geometry and `classical' gauge theory.

· Inventiones Mathematicæ 119 (1995), 155-163.

· Review (from Zentralblatt).

· Cited in [Akbulut & Matveyev 1997], [Akbulut & Ozbagci 2001], [Baader 2005a, 2006a], [Baader & Ishikawa 2006], [Boileau & Fourrier 1998], [Cha 2006], [Cimasoni 2006], [Dunfield, Gukov & Rasmussen 2005], [Ekholm, Etnyre & Sullivan 2005], [Etnyre 1998, 1999, 2000, 2005], [Etnyre & Ghrist 2002], [Etnyre & Honda 2001ab], [Etnyre & Ng, 2003], [Etnyre, Ng, & Sabloff 2002], [Ferrand 1999, 2002, 2005], [Gompf 1998ab], [Guilfoyle 2006], [Hedden 2005, 2006], [Ishikawa 2001ab, 2005], [Kirby 1997], [Kirk & Livingston 2001], [Manolescu & Owens 2007], [Matsuda 2006], [Ng 2001b], [Ozsvath, Szabo, & Thurston 2006], [Przytycki 1997], [Shumakovitch 2004], [Stoimenow 2000a, 2006d], [Tanaka 1999b, 2006], [Torisu 2001], [Traynor 1998].

[1995c] How Hard Is It to Untie a Knot? (with William Menasco).

· The American Scientist 83 (1995), 38-49.

· Abstract and sample illustration; a related illustration; full text and illustrations (available for a fee from HighBeam Research); short summary by Allyn Jackson published in What's New in Math (American Mathematical Society).

· Cited in [Casti 2000], [Gardner 1997, 2001], [Root-Bernstein 1996], [Taylor et al. 2003], [Trinajstic & Gutman 2002].

[1995d] Two remarks on the Thurston-Bennequin invariant. (Preprint; subsumed into [Rudolph 1997].)

· Cited in [Eliashberg & Fraser 1998].

[1993] Quasipositivity as an obstruction to sliceness.

· Bulletin of the American Mathematical Society 29 (1993), 51-59.

· Review (from Zentralblatt).

· Cited in [Baader 2005c, 2007], [Bizaca 1995], [Bizaca & Gompf 1996], [Bohr 2002], [Bohr & Lee 2002], [Boileau & Fourrier 1998], [Burde & Zieschang 2003], [Cimasoni 2006], [Diao, Ernst & Stasiak 2006], [Dasbach & Mangum 2001], [Ferrand 1999, 2002, 2005], [Gompf & Stipsicz 1999], [Hedden 2005, 2006], [Hirasawa 2001], [Ishikawa 2001, 2005], [Kamada 1996a], [Kawamura 1998, 2000, 2001, 2002abc, 2004, 2005, 2007], [Kawauchi 1996], [Kirby 1997], [Kotschick & Matic 1995], [Lee & Wilczynski 1997], [Lisca & Stipsicz 2006], [Livingston 2005a], [Nakamura 2000], [Ng 2001b, 2005], [Orevkov 2000b], [Oszvath & Szabo 2003, 2004, 2005], [Plamenevskaya 2006, 2007], [Shumakovitch 2004], [Silver & Whitten 2005], [Stoimenow 2000a, 2001b, 2002d, 2003bd, 2004a, 2005, 2006abc], [Tanaka 1998ab, 1999a], [Torisu 2003], [Van Cott 2006], [Ville 2007], [Wu 2006, 2007], [Yamada 2005].

[1992a] Totally tangential links of intersection of complex plane curves with round spheres.

· Topology'90 (Proceedings of the Ohio State University Topology Research Semester), ed. L. Siebenmann et al. ( DeGruyter, 1992), 343-349.

· Review (from Zentralblatt).

· Cited in [Ferrand 2002, 2005], [Kamada 2002], [Kawamura 2002b, 2004, 2006], [Kawauchi 1996], [Traynor 1998].

[1992b] Quasipositive annuli (Constructions of quasipositive knots and links, IV).

· Journal of Knot Theory and its Ramifications 1 (1992), 451-466.

· Review (from Zentralblatt).

· Cited in [Akbulut & Ozbagci 2001], [Bae, Kim, & Park 2006], [Boileau & Fourrier 1998], [Cromwell 2004], [Ferrand 1999], [Gompf 1998a], [Kim & Lee 2007], [Nutt 1995, 1997, 1999], [Stoimenow 2000a], [Tanaka 1998b], [Wu 2007].

[1992c] A characterization of quasipositive Seifert surfaces (Constructions of quasipositive knots and links, III).

· Topology 31 (1992), 231-237.

· Review (from Zentralblatt).

· Cited in [Akbulut & Ozbagci 2001], [Baader, Cieliebak, & Vogel 2007], [Boileau & Fourrier 1998], [Kamada 1996a], [Ko & Lee 1997], [Tanaka 1998b].

[1991] The structure of orthogonal transformations.

· American Mathematical Monthly 98 (1991), 349-352.

· On-line version (available only via JSTOR subscription).

· Review (from Zentralblatt).

· Cited in [Aragon-Gonzales et al. 2006].

[1990a] Difference index of vectorfields and the enhanced Milnor number (with W. D. Neumann).

· Topology 29 (1990), 83-100.

· Review (from Zentralblatt).

· Cited in [Cimasoni 2002, 2004a], [Etnyre & Ozbagci 2008], [2006], [Kirby 1997], [Neumann 1999].

[1990b] A congruence between link polynomials.

· Mathematical Proceedings of the Cambridge Philosophical Society 107 (1990), 319-327.

· Review (from Zentralblatt).

· Cited in [Boileau & Fourrier 1998], [Chmutov & Gorynov 1997], [Etnyre 2005], [Ferrand 2002], [Fuchs & Tabachnikov 1997], [Goryunov 2001], [Gruber 2004], [Kalfagianni and Lin 2007], [Kálmán 2006], [Kerr 2004], [Kirby 1997], [Mohnke 2000], [Morton 2007], [Morton & Beltrami 1998], [Nakamura 2002, 2006], [Ng 2001ab, 2005, 2006], [Nutt 1997, 1999], [Stoimenow 2004b].

[1989] Quasipositivity and new knot invariants.

· Revista Matemática de la Universidad Complutense de Madrid 2 (1989), 85-109.

· Review (from Zentralblatt).

[1988a] Mutually braided open books and new invariants of fibered links.

· Braids (Contemporary Mathematics 78), ed. J. Birman, A. Libgober (American Mathematical Society, Providence, 1988), 657-674.

· Review (from Zentralblatt).

· Cited in [Bae, Kim, & Park 2006], [Morton & Rampichini 2000], [Rampichini 1999, 2001].

[1988b] The enhanced Milnor number in higher dimensions (with W. D. Neumann).

· Differential Topology (Lecture Notes in Mathematics 1350), ed. U. Koschorke (Springer, New York, 1988), 109-121.

· Review (from Zentralblatt).

· Cited in [Giroux & Goodman 2006], [Kirby 1997], [Neumann 1999].

[1987a] Unfoldings in knot theory (with W. D. Neumann); corrigendum.

· Mathematische Annalen 278 (1987), 409-439.

· Review (from Zentralblatt).

· Cited in [Abhyankar & Sathaye 1996], [Bodin 1999, 2002], [Boileau & Fourrier 1998], [Brélivet 2005], [Cassou-Nogues 1996], [Cimasoni 2002, 2004b], [Dimca 1998], [Fourrier 1996], [Giroux 2003], [Giroux & Goodman 2006], [Goodman 2003], [Gwozdziewicz & Ploski 2000] [Kaliman 1993], [Kirby 1997], [Libgober 1993], [Nemethi & Zaharia 1992], [Nemethi 1991], [Neumann 1989], [Neumann & Norbury 2000, 2001], [Nowicki 1997], [Saeki 1999].

[1987b] Isolated critical points of mappings from R⁴ to R² and a natural splitting of the Milnor number of a classical fibered link. Part I: Basic theory; examples.

· HyperTeXed ArXival version (correcting minor typographical errors; with addenda).

· Commentarii Mathematici Helvetici 62 (1987), 630-645.

· Review (from Zentralblatt).

· Cited in [Benedetti & Shiota 1998], [Goodman 2003], [Kirby 1997], [Neumann 1989], [Pichon 2005], [Ville 2007], [Winkelnkemper 1998].

[1986] Isolated critical points of mappings from R⁴ to R² and a natural splitting of the Milnor number of a classical fibered link. Part II

· Geometry & Topology: Manifolds, Varieties, and Knots, ed. C. McCrory, T. Shifrin (Marcel Dekker, New York, 1986), 251-263.

· Review (from Zentralblatt).

[1985a] Plane curves in fancy balls.

· L'Enseignement Mathématique 31 (1985), 81-84.

· Review (from Zentralblatt).

[1985b] Special positions for surfaces bounded by closed braids.

· Revista Matemática Iberoamericana 1 (1985), 93-133.

· Cited in [Birman & Menasco 1991, 1992a], [Boileau & Fourrier 1998], [Hasegawa 2004], [Kamada 1994ab, 1996ab, 1998, 1999], [Kamada & Matsumoto 2005], [Morton 1983], [Piergallini & Zuddas 2001], [Rampichini 2001], [Tanaka 2005], [Zuddas 2000, 2007, 2007].

[1984a] Some topologically locally-flat surfaces in the complex projective plane.

· Commentarii Mathematici Helvetici 59 (1984), 592-599.

· Review (from Zentralblatt).

· Cited in [Bennequin 1990], [Donaldson 1988], [Kamada 1996ab], [Kamada, Satoh, & Takabayashi 2006], [Kirby 1997], [Kotschick & Matic 1995], [Lee & Wilczynski 1997], [Livingston 2004], [Stoimenow 2001e] [Tanaka 1998a].

[1984b] Constructions of quasipositive knots and links, II.

· Four-Manifold Topology (Contemporary Mathematics, 35), ed. C. Gordon, R. Kirby (American Mathematical Society, Providence, 1984), 485-491.

· Cited in [Boileau & Fourrier 1998], [Ferrand 2002], [Tanaka 1998b].

[1983a] Some knot theory of complex plane curves.

· HyperTeXed ArXival version.

· L'Enseignement Mathématique 29 (1983), 185-208.

· Illustrations.

· Cited in [Cohen & Suciu 1997], [Fiedler 1989, 1991], [Hirasawa, Murasugi & Silver 2007], [Kronheimer & Mrowka 1993], [Orevkov 2000a], [Ville 2007].

[1983b] Constructions of quasipositive knots and links, I.

· Noeuds, Tresses, et Singularités (Monographie No. 31 de L'Enseignement Mathématique), ed. C. Weber (Kundig, Geneva, 1983), 233-246.

· Cited in [Fiedler 1989], [Kawamura 2001c], [Rampichini 2001], [Skora 1992], [Sundheim 1993].

[1983c] Nontrivial positive braids have positive signature.

· Topology 21 (1983), 325-327.

· Cited in [Birman & Williams 1983], [Cochran & Gompf 1988], [Gordon 1981], [Murasugi 1989], [Stoimenow 2000b, 2006b], [Traczyk 1988], [van Buskirk 1985].

[1983d] Algebraic functions and closed braids.

· Topology 22 (1983), 191-202.

· Cited in [Bohr 2001], [Boileau & Fourrier 1998], [Carter & Saito 1996], [Dung 1999], [Ishikawa 2001] [Jones 1987], [Kamada 1996ab], [Kawamura 2001c, 2006], [Kirby 1997], [Ko & Lee 1997], [Libgober 1987], [Loi & Piergallini 2001], [Nakamura 2000], [Orevkov 1988, 1996, 1998, 1999, 2000a], [Piergallini & Zuddas 2001, 2005], [Tanaka 1998ab], [Trilles 2000], [Zuddas 2007].

[1983e] Braided surfaces and Seifert ribbons for closed braids.

· Commentarii Mathematici Helvetici 58 (1983), 1-37.

· Review of a related paper (from Zentralblatt).

· Cited in [Bae, Kim, & Park 2006], [Birman, Ko, & Lee 1998], [Birman & Menasco 1992, 1993], [Boileau & Weber 1983], [Boileau & Fourrier 1998], [Carrara, Carter & Saito 2001], [Carter, Jelsovsky, Kamada, Langford, & Saito 1999, 2001], [Carter, Kamada, & Saito 2000], [Carter & Saito 1996], [Cerne 2000], [Fiedler 1991, 1993], [Franks & Williams 1987], [Hirasawa 2007], [Kamada 1994, 1996ab, 1998, 1999], [Kawamura 2000b], [Khovanov & Thomas 2007], [Ko & Lee 1997], [Loi & Piergallini 2001], [Morton 1983], [Morton & Rampichini 2000] [Nakamura 2000], [Piergallini & Zuddas 2001], [Popescu 2007], [Stoimenow 2001ce, 2002bc], [Wright 2000], [Zuddas 2000, 2007].

[1982] Embeddings of the line in the plane.

· Journal für die reine und angewandte Mathematik 337 (1982), 113-118.

· Cited in [Abhyankar & Sathaye 1991], [Chang & Wang 1993], [Artal Bartolo 1995], [Bodin 2002, 2008], [Boileau & Fourrier 1998], [Fourrier 1994, 1996], [Gurjar & Miyanishi 1996], [Kang 1991], [Kirby 1997], [Kraft 1996], [Tibar 2007].

[1979] The modular symbol and continued fractions in higher dimensions (with Avner Ash).

· Inventiones Mathematicæ 55 (1979), 241-250.

· Cited in [Allison, Ash, & Conrad 1998], [Ash 1983, 1986, 1988, 1989, 1994], [Ash, Grayson, & Green 1984], [Ash, Gunnells, & McConnell 2002], [Ash & McConnell 2002], [Broaddus 2007],:w [Chinta, Gunnells, & Sczech 2000], [van Geemen, van der Kallen, Top, & Verberkmoes 1997] [van Geemen & Top 2000], [Goldfeld & Gunnells 2000], [Gunnells 1999, 2000abcd], [Gunnells & McConnell 2003], [Gunnells & Sczech 2003], [Lee & Schwermer 1986], [Reeder 1990, 1991], [Sczech 1993], [Schmidt 1993], [Stein 2006].

[1976a] Comparing the topological and analytic classification of germs of analytic plane curves.

· Brown University preprint (1976).

· Cited in [Bruce & Gaffney 1982].

[1976b] How independent are the knot-cobordism classes of links of plane curve singularities?

· Question in "Queries" column, Notices Amer. Math. Soc. 23 (1976), 410 (from a problem list compiled at the Special Session on Knot Theory, 1976 Summer Meeting of A.M.S., Toronto).

· Cited in [Litherland 1979], [Livingston & Melvin 1983].

[1975a] A Morse function for a surface in CP³.

· Topology 14 (1975), 301-303.

· Cited in [Harer 1978], [Harer, Kas, & Kirby 1986], [Kirby 1997], [Kulkarni & Wood 1980], [Mandelbaum 1979, 1980ab].

[1975b] Velocity space and the geometry of planetary orbits (with Harold Abelson & Andrea di Sessa).

· American Journal of Physics 43 (1975), 579-589.

· Cited in [Butikov 2000], [Calkin 1996], [Clement & Lochhead 1979], [Derbes 2001], [di Sessa 1980], [Dumais 1979], [Guillaumín-España, Salas-Brito, & Núñéz-Yepez 2003], [Hollerbach 1981], [Munoz 2003], [Patera 1978, 1981], [Patera & Schreurs 1980], [Rainwater & Weinstock 1979], [Peters 1991], [Shore 1989], [Wheeler 2005].

[1974] LOGO Manual (with Harold Abelson & Nat Goodman).

· LOGO Memo 7 (AI Memo 313), M.I.T. Artificial Intelligence Laboratory, December 1974.

· Cited in [Cointe 1984], [Curado & Valente 1978], [Lieberman 1976], [Solomon 1976], [Trollip & Ortony 1977].

[1970] Calculus of Elementary Functions (with Harold Abelson & Leonard Fellman).

· Harcourt Brace Jovanovich, New York, 1970.