A family of transverse link homologies

Wu, Hao¹

¹Department of Mathematics, The George Washington University, Monroe Hall, Room 240, 2115 G Street, NW, Washington DC 20052, USA

Algebraic and Geometric Topology, Tome 16 (2016) no. 1, pp. 41-127

Résumé

We define a homology ℋN for closed braids by applying Khovanov and Rozansky’s matrix factorization construction with potential axN+1. Up to a grading shift, ℋ0 is the HOMFLYPT homology defined by Khovanov and Rozansky. We demonstrate that for N ≥ 1, ℋN is a ℤ2 ⊕ ℤ⊕3–graded ℚ[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 ℋN and the relation between ℋN and the sl(N) Khovanov–Rozansky homology.

Détail

DOI : 10.2140/agt.2016.16.41

Classification : 57M25, 57R17
Keywords: transverse link, Khovanov–Rozansky homology, HOMFLYPT polynomial

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