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The slice genus and the Thurston-Bennequin invariant of a knot

Author(s): Lee Rudolph
Journal: Proc. Amer. Math. Soc. 125 (1997), 3049-3050.
MSC (1991): Primary 57M25; Secondary 14H99
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Abstract: For any knot $K\subset S^{3}$ , $g_{s}(K) \ge (\operatorname {TB}(K)+1)/2$ .

References:

1.: D. Bennequin, Entrelacements et équations de Pfaff, Astérisque 107-8 (1983), 87-161. MR 86e:58070
2.: P. Kronheimer & T. Mrowka, Gauge theory for embedded surfaces, I, Topology (1993). MR 94k:57048
3.: -, personal communication, December 11, 1995.
4.: Lee Rudolph, An obstruction to sliceness via contact geometry and ``classical'' gauge theory, Invent. Math. 119 (1995), 155-163. MR 95k:57013
5.: -, Quasipositivity as an obstruction to sliceness, Bull. Amer. Math. Soc. 29 (1993), 51-59. MR 94d:57028

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Additional Information:

Lee Rudolph
Affiliation: Department of Mathematics and Computer Science, Clark University, Worcester, Massachusetts 01610
Email: lrudolph@black.clarku.edu

DOI: 10.1090/S0002-9939-97-04258-5
PII: S 0002-9939(97)04258-5
Keywords: Slice genus, Thom Conjecture, Thurston-Bennequin invariant
Received by editor(s): October 12, 1995
Additional Notes: The author was partially supported by NSF grant DMS-9504832 and CNRS
Communicated by: Ronald Stern
Copyright of article: Copyright 1997, American Mathematical Society

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