Mathematical Publications of Lee Rudolph

[Final update on aleph0, June 21, 2002; if you were not automatically redirected to http://black.clarku.edu/~lrudolph/research/mathpubs.htm, you should do so yourself.]
[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, to appear (2002).
· Publisher's on-line version (abstract available to all comers, full text to AMS subscribers only).
· 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).
· St. Petersburg Mathematical Journal [cover-to-cover translation of Algebra i Analiz] 13 (2001), 105-118.
[2001b] Hopf plumbing, baskets, arborescent Seifert surfaces, espaliers, and homogeneous braids.
· Topology and its Applications 116 (2001), 255-277.
· Illustrations.
[2001c] Quasipositive pretzels.
· Topology and its Applications 115 (2001), 115-123.
· Publisher's on-line version (Elsevier subscribers only).
· Review (from Zentralblatt).
[2001d] Murasugi sums of Morse maps to the circle, Morse-Novikov numbers, and free genus of knots.
· Illustrations.
[1999] Positive links are strongly quasipositive.
· Geometry and Topology Monographs 2 [Proceedings of the Kirbyfest] (1999), 555-562.
· Review (from Zentralblatt).
· Cited in [Bohr 2001], [Dasbach & Mangum 2001], [Hirasawa 2001], [Kawamura 2000b], [Nakamura 2000], [Stoimenow 2000c, 2001abce, 2002c].
[1998] Quasipositive plumbing (Constructions of quasipositive knots and links, V).
· Proceedings of the American Mathematical Society 126 (1998), 257-267.
· Publisher's on-line version (abstract available to all comers, full text to AMS subscribers only).
· Review (from Zentralblatt).
· Illustrations.
· Cited in [Akbulut & Ozbagci 2001], [Birman, Boldi, Rampichini, & Vigna 2001], [Boileau & Fourrier 1998], [Tanaka 1998ab].
[1997] The slice genus and the Thurston-Bennequin invariant of a knot.
· Proceedings of the American Mathematical Society 125 (1997), 3049-3050.
· Publisher's on-line version (abstract available to all comers, full text to AMS subscribers only).
· Cited in [Traynor 1998].
[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], [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], [Etnyre 1998, 1999, 2000], [Etnyre & Ghrist 2002], [Etnyre & Honda 2000, 2001], [Etnyre & Ng, 2002], [Etnyre, Ng, & Sabloff 2001], [Gompf 1998], [Kirby 1997], [Tanaka 1999, 2000], [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 Northern Light); short summary by Allyn Jackson published in What's New in Math (American Mathematical Society).
· Cited in [Gardner 1997], [Root-Bernstein 1996].
[1993] Quasipositivity as an obstruction to sliceness.
· Bulletin of the American Mathematical Society 29 (1993), 51-59.
· Review (from Zentralblatt).
· Cited in [Bizaca & Gompf 1996], [Bizaca 1995], [Bohr 2001], [Boileau & Fourrier 1998], [Dasbach & Mangum 2001], [Ferrand 1999], [Hirasawa 2001], [Ishikawa 2001], [Kamada 1996ab], [Kawamura 1998, 2000b, 2001c], [Kirby 1997], [Kotschick & Matic 1995], [Lee & Wilczynski 1997], [Nakamura 2000], [Orevkov 2000b], [Stoimenow 2001ce, 2002b].
[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 [Kawamura 2001c], [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], [Gompf 1998], [Nutt 1997,1999].
[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], [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).
[1990a] Difference index of vectorfields and the enhanced Milnor number (with W. D. Neumann).
· Topology 29 (1990), 83-100.
· Review (from Zentralblatt).
· Cited in [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], [Fuchs & Tabachnikov 1997], [Goryunov 2001], [Kirby 1997], [Mohnke 2000], [Morton & Beltrami 1998], [Nutt 1997, 1999].
[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 [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 [Kirby 1997], [Neumann 1999].
[1987a] Unfoldings in knot theory (with W. D. Neumann).
· Mathematische Annalen 278 (1987), 409-439.
· Review (from Zentralblatt).
· Cited in [Abhyankar & Sathaye 1996], [Bodin 2002], [Boileau & Fourrier 1998], [Cassou-Nogues 1996], [Dimca 1998], [Fourrier 1996], [Gwozdziewicz & Ploski 2000] [Kaliman 1993], [Kirby 1997], [Libgober 1993], [Nemethi & Zaharia 1992], [Nemethi 1991], [Neumann 1989], [Neumann & Norbury 2000, 2001].
[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.
· Commentarii Mathematici Helvetici 62 (1987), 630-645.
· Review (from Zentralblatt).
· Cited in [Benedetti & Shiota 1998], [Kirby 1997], [Neumann 1989].
[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], [Kamada 1994ab, 1996ab, 1998, 1999], [Morton 1983], [Piergallini & Zuddas 2001], [Rampichini 2001], [Zuddas 2000].
[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], [Kirby 1997], [Kotschick & Matic 1995], [Lee & Wilczynski 1997], [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], [Tanaka 1998b].
[1983a] Some knot theory of complex plane curves.
· L'Enseignement Mathématique 29 (1983), 185-208.
· Illustrations.
· Cited in [Cohen & Suciu 1997], [Fiedler 1989, 1991], [Kronheimer & Mrowka 1993], [Orevkov 2000a].
[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], [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], [Kirby 1997], [Ko & Lee 1997], [Libgober 1987], [Loi & Piergallini 2001], [Nakamura 2000], [Orevkov 1988, 1996, 1998, 1999, 2000a], [Piergallini & Zuddas 2001], [Tanaka 1998ab].
[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 [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], [Kamada 1994, 1996ab, 1998, 1999], [Kawamura 2000b], [Ko & Lee 1997], [Loi & Piergallini 2001], [Morton 1983], [Morton & Rampichini 2000] [Nakamura 2000], [Piergallini & Zuddas 2001], [Stoimenow 2001ce, 2002bc], [Wright 2000], [Zuddas 2000].
[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], [Boileau & Fourrier 1998], [Fourrier 1994, 1996], [Gurjar & Miyanishi 1996], [Kang 1991], [Kirby 1997], [Kraft 1996].
[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 2000], [Chinta, Gunnells, & Sczech 2000], [van Geemen, van der Kallen, Top, & Verberkmoes 1997] [van Geemen & Top 2000], [Goldfeld & Gunnells 2000], [Gunnells 1999, 2000ad], [Gunnells & McConnell 1998], [Reeder 1990, 1991], [Sczech 1993], [Schmidt 1993].
[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 [Derbes 2001], [Peters 1991], [Shore 1989].
[1970] Calculus of Elementary Functions (with Harold Abelson & Leonard Fellman), Harcourt Brace Jovanovich, New York, 1970.