Abstract
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.
Citation
Hao Wu. "A family of transverse link homologies." Algebr. Geom. Topol. 16 (1) 41 - 127, 2016. https://doi.org/10.2140/agt.2016.16.41
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