In , 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 ) of the Khovanov complex and another as a cohomotopy element of the Khovanov spectrum (from ). 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