On transverse invariants from Khovanov homology

Robert Lipshitz, Lenhard Ng, Sucharit Sarkar
2015 Quantum Topology  
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
more » ... transverse knots K, both refinements are determined by the classical invariants of K.
doi:10.4171/qt/69 fatcat:5ujk6edgunbqjpwm6x2k525swm