Totally twisted Khovanov homology

Andrew Manion (Princeton)

Abstract: The construction of totally twisted Khovanov homology, by Lawrence Roberts, yields a chain complex whose homology contains the same data as the usual Khovanov homology for knots (by work of Jaeger). The complex is generated by spanning trees of the Tait graph of a knot diagram, and the matrix coefficients of the differential can be written down explicitly. It was originally defined over Z/2; I'll review this construction and discuss how to define it over Z to compute odd Khovanov homology for knots.