An odd analog of Plamenevskaya's invariant of transverse knots

Abstract

Plamenevskaya defined an invariant of transverse links as a distinguished class in the even Khovanov homology of a link. We define an analog of Plamenevskaya's invariant in the odd Khovanov homology of Ozsv\'ath, Rasmussen, and Szab\'o. We show that the analog is also an invariant of transverse links and has similar properties to Plamenevskaya's invariant. We also show that the analog invariant can be identified with an equivalent invariant in the reduced odd Khovanov homology. We demonstrate computations of the invariant on various transverse knot pairs with the same topological knot type and self-linking number.