Mathematics Seminar Series: Groups, Geometry, and Topology

Abstract: Odd Khovanov homology, discovered by Ozsváth-Rasmussen-Szabó, is a link homology theory that categorifies the Jones polynomial. It is closely related to Khovanov homology, but it also has an extra suspected connection with Heegaard Floer homology. We investigate a space-level lift of odd Khovanov homology, called the odd Khovanov spectrum, and classify this space for all prime knots up to 11 crossings using the second Steenrod square. In the process, we discover unexpected results regarding this space's behavior, and also uncover multiple types of even and odd Khovanov spectra.