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


In [31], O. Plamenevskaya associated to each transverse knot an element of the Khovanov homology of . 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 moves; this implies that Plamenevskaya’s class is also invariant under these moves. We go on to show that for small-crossing transverse knots , both renements are determined by the classical invariants of .

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