Braids, Transversal links and the Khovanov-Rozansky Theory

Abstract

We establish some inequalities about 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 is 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.

26 pages, 15 figures. Third version: modified proofs of Lemma 3.1 and Proposition 4.2, also corrected some typos and inconsistency in conventions

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