A novel approach to odd Khovanov homology

Khovanov homology is a homological invariant of knots stemming from representation theory, powerful enough to detect exotic phenomenas. In an attempt to relate Khovanov homology to Heegaard–Floer homology over the integers, Osváth, Rasmussen and Szabó discovered a variant "with signs" of Khovanov homology, called odd Khovanov homology. Unfortunately, the intricate use of signs in its definition has left odd Khovanov homology much less understood than its even counterpart. In this talk, we will give a new definition of odd Khovanov homology by relating it to representation theory. This gives an extension of odd Khovanov homology to tangles, but perhaps more importantly, provides a conceptual definition where signs are now controlled by the categorical analogue of a superalgebra. This is partially joint with Pedro Vaz.