Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 1 (2016), 41-127.
A family of transverse link homologies
We define a homology for closed braids by applying Khovanov and Rozansky’s matrix factorization construction with potential . Up to a grading shift, is the HOMFLYPT homology defined by Khovanov and Rozansky. We demonstrate that for , is a –graded –module that is invariant under transverse Markov moves, but not under negative stabilization/destabilization. Thus, for , this homology is an invariant for transverse links in the standard contact , but not for smooth links. We also discuss the decategorification of and the relation between and the Khovanov–Rozansky homology.
Algebr. Geom. Topol., Volume 16, Number 1 (2016), 41-127.
Received: 8 April 2014
Revised: 12 February 2015
Accepted: 15 April 2015
First available in Project Euclid: 16 November 2017
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Wu, Hao. A family of transverse link homologies. Algebr. Geom. Topol. 16 (2016), no. 1, 41--127. doi:10.2140/agt.2016.16.41. https://projecteuclid.org/euclid.agt/1510841104