A family of transverse link homologies

作者：Wu Hao^*

来源：Algebraic and Geometric Topology, 2016, 16(1): 41-127.

DOI：10.2140/agt.2016.16.41

We define a homology H-N for closed braids by applying Khovanov and Rozansky's matrix factorization construction with potential ax(N+1). Up to a grading shift, H-0 is the HOMFLYPT homology defined by Khovanov and Rozansky. We demonstrate that for N >= 1, H-N is a Z(2)circle plus Z(circle plus 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 S-3, but not for smooth links. We also discuss the decategorification of H-N and the relation between H-N and the sl(N) Khovanov-Rozansky homology.

• 出版日期2016