Geometry and Topology Seminar: Doubled Khovanov homology
19 October 2017 13:00 in CM221
Virtual knot theory is an extension of classical knot theory which considers knots and links in equivalence classes of thickened orientable surfaces.
Khovanov homology is a powerful invariant of classical links, and it can be applied to virtual links using Z_2 coefficients. However, a number of problems arise when one attempts to use other coefficient rings. In this talk we describe doubled Khovanov homology: an extension of Khovanov homology to virtual links with arbitrary coefficients. Unlike other extensions of Khovanov homology, doubled Khovanov homology requires no new diagrammatics, as all the work is done algebraically. We shall describe the construction of the invariant as well as some of its applications, in particular to virtual knot concordance.