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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: 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 $ S^3$ 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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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
Published electronically: February 27, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.