Algebraic & Geometric Topology

A family of transverse link homologies

Hao Wu

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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.

Article information

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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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57R17: Symplectic and contact topology

transverse link Khovanov–Rozansky homology HOMFLYPT polynomial


Wu, Hao. A family of transverse link homologies. Algebr. Geom. Topol. 16 (2016), no. 1, 41--127. doi:10.2140/agt.2016.16.41.

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