A New Spectral Sequence in Khovanov Homology

A New Spectral Sequence in Khovanov Homology

-
Cotton Seed, Princeton University
Fine Hall 314

Khovanov homology is an invariant of links L in S^3which categorifies the Jones polynomial. In this talk, I will describe a new spectral sequence in Khovanov homology, the link forgetful spectral sequence. The spectral sequence starts at Khovanov homology and converges to the Khovanov homology of the disjoint union of the components of the link -- that is, it forgets the linking between components. The discovery of this construction was partly motivated by looking for an analog in Khovanov homology of the component-forgetting spectral sequence in link Floer homology. As an application, building on results of Kronheimer-Mrowka and Hedden-Ni, I will prove that Khovanov homology detects the unlink. Joint work with Josh Batson.