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A family of transverse link homologies

Hao Wu

Algebraic & Geometric Topology 16 (2016) 41–127
Abstract

We define a homology N for closed braids by applying Khovanov and Rozansky’s matrix factorization construction with potential axN+1. Up to a grading shift, 0 is the HOMFLYPT homology defined by Khovanov and Rozansky. We demonstrate that for N 1, N is a 2 3–graded [a]–module that is invariant under transverse Markov moves, but not under negative stabilization/destabilization. Thus, for N 1, this homology is an invariant for transverse links in the standard contact S3, but not for smooth links. We also discuss the decategorification of N and the relation between N and the sl(N) Khovanov–Rozansky homology.

Keywords
transverse link, Khovanov–Rozansky homology, HOMFLYPT polynomial
Mathematical Subject Classification 2010
Primary: 57M25, 57R17
References
Publication
Received: 8 April 2014
Revised: 12 February 2015
Accepted: 15 April 2015
Published: 23 February 2016
Authors
Hao Wu
Department of Mathematics
The George Washington University
Monroe Hall, Room 240
2115 G Street, NW
Washington DC 20052
USA