On transverse invariants from Khovanov homology

Robert Lipshitz; Lenhard Ng; Sucharit Sarkar

doi:10.4171/qt/69

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arXiv · 1303.6371

On transverse invariants from Khovanov homology

Robert Lipshitz·Lenhard Ng·Sucharit Sarkar

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Abstract

O. Plamenevskaya associated to each transverse knot K an element of the Khovanov homology of K. In this paper, we give two refinements of Plamenevskaya's invariant, one valued in Bar-Natan's deformation of the Khovanov complex and another as a cohomotopy element of the Khovanov spectrum. We show that the first of these refinements is invariant under negative flypes and SZ moves; this implies that Plamenevskaya's class is also invariant under these moves. We go on to show that for small-crossing transverse knots K, both refinements are determined by the classical invariants of K.

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Robert Lipshitz, Lenhard Ng, Sucharit Sarkar. 2013-03-26. On transverse invariants from Khovanov homology. https://doi.org/10.4171/qt%2F69

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