Volume 16, issue 1 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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