JournalsqtVol. 6 , No. 3pp. 475–513

On transverse invariants from Khovanov homology

  • Robert Lipshitz

    Columbia University, New York, USA
  • Lenhard L. Ng

    Duke University, Durham, USA
  • Sucharit Sarkar

    Princeton University, USA
On transverse invariants from Khovanov homology cover
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Abstract

In [31], O. Plamenevskaya associated to each transverse knot KK an element of the Khovanov homology of KK. In this paper, we give two renements of Plamenevskaya’s invariant, one valued in Bar-Natan’s deformation (from [2]) of the Khovanov complex and another as a cohomotopy element of the Khovanov spectrum (from [20]). We show that the rst of these renements is invariant under negative ypes and SZSZ moves; this implies that Plamenevskaya’s class is also invariant under these moves. We go on to show that for small-crossing transverse knots KK, both renements are determined by the classical invariants of KK.

Cite this article

Robert Lipshitz, Lenhard L. Ng, Sucharit Sarkar, On transverse invariants from Khovanov homology. Quantum Topol. 6 (2015), no. 3 pp. 475–513

DOI 10.4171/QT/69