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Braids, transversal links and the Khovanov-Rozansky Theory
Author:
Hao Wu
Journal:
Trans. Amer. Math. Soc. 360 (2008), 3365-3389
MSC (2000):
Primary 57M25, 57R17
Posted:
February 27, 2008
MathSciNet review:
2386230
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Abstract: We establish some inequalities for the Khovanov-Rozansky cohomologies of braids. These give new upper bounds of the self-linking numbers of transversal links in standard contact  which are sharper than the well-known bound given by the HOMFLY polynomial. We also introduce a sequence of transversal link invariants and discuss some of their properties.
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- 1.
- D. Bar-Natan, Khovanov's homology for tangles and cobordisms, Algebr. Geom. Topol. 9 (2005), 1443-1499 (electronic). MR 2174270 (2006g:57017)
- 2.
- D. Bennequin, Entrelacements et équations de Pfaff, Astérisque 107-108 (1983), 87-161. MR 753131 (86e:58070)
- 3.
- E. Ferrand, On Legendrian knots and polynomial invariants, Proc. Amer. Math. Soc. 130 (2002), no. 4, 1169-1176 (electronic). MR 1873793 (2002j:57047)
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- J. Franks, R. F. Williams, Braids and the Jones polynomial, Trans. Amer. Math. Soc. 303 (1987), no. 1, 97-108. MR 896009 (88k:57006)
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- D. Fuchs, S. Tabachnikov, Invariants of Legendrian and transverse knots in the standard contact space, Topology 36 (1997), no. 5, 1025-1053. MR 1445553 (99a:57006)
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- M. Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000), no. 3, 359-426. MR 1740682 (2002j:57025)
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- M. Khovanov, L. Rozansky, Matrix factorizations and link homology, arXiv:math.QA/ 0401268.
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- M. Khovanov, L. Rozansky, Matrix factorizations and link homology II, arXiv:math.QA/ 0505056.
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- H. Morton, Seifert circles and knot polynomials, Math. Proc. Cambridge Philos. Soc. 99 (1986), no. 1, 107-109. MR 809504 (87c:57006)
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- S. Orevkov, V. Shevchishin, Markov theorem for transversal links, J. Knot Theory Ramifications 12 (2003), no. 7, 905-913. MR 2017961 (2004j:57011)
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- O. Plamenevskaya, Transverse knots and Khovanov homology, Math. Res. Lett. 13 (2006), 571-586. MR 2250492 (2007d:57043)
- 12.
- N. Wrinkle, The Markov Theorem for transverse knots, arXiv:math.GT/0202055.
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Additional Information
Hao Wu
Affiliation:
Department of Mathematics and Statistics, Lederle Graduate Research Tower, 710 North Pleasant Street, University of Massachusetts, Amherst, Massachusetts 01003-9305
Address at time of publication:
Department of Mathematics, The George Washington University, Monroe Hall, Room 240, 2115 G Street, N.W., Washington, DC 20052
Email:
wu@math.umass.edu, haowu@gwu.edu
DOI:
http://dx.doi.org/10.1090/S0002-9947-08-04339-0
PII:
S 0002-9947(08)04339-0
Keywords:
Braid,
transversal knot,
knot homology,
matrix factorization
Received by editor(s):
January 20, 2006
Received by editor(s) in revised form:
May 24, 2006
Posted:
February 27, 2008
Article copyright:
© Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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