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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A Legendrian Thurston–Bennequin bound from Khovanov homology

Lenhard Ng

Algebraic & Geometric Topology 5 (2005) 1637–1653

arXiv: math.GT/0508649

Abstract

We establish an upper bound for the Thurston–Bennequin number of a Legendrian link using the Khovanov homology of the underlying topological link. This bound is sharp in particular for all alternating links, and knots with nine or fewer crossings.

Keywords
Legendrian link, Thurston–Bennequin number, Khovanov homology, alternating link
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57R17, 53D12
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Publication
Received: 16 September 2005
Accepted: 21 November 2005
Published: 25 November 2005
Authors
Lenhard Ng
Department of Mathematics
Stanford University
Stanford CA 94305
USA
http://alum.mit.edu/www/ng/