Department of Mathematics - Master Calendar

Khovanov homology assigns a graded chain complex of vector spaces to a link or a tangle. The construction categorifies the Jones polynomial, by taking the Euler characteristic of the Khovanov homology.  Lipshitz—Sarkar and Hu--Kriz—Kriz construct a spectrum associated to a link whose homology is Khovanov homology and these constructions are proved to be equivalent by Lawson--Lipshitz—Sarkar. Spectra associated to tangles are later constructed by Lawson--Lipshitz—Sarkar. On the other hand, there is a sign discrepancy of Khovanov homology that two movies representing equivalent cobordisms induce homotopy equivalent chain maps only up to sign. In this talk, I will give an overview of this subject and describe an ongoing work on how to fix the sign on the spectrum level. This is an ongoing joint work by Anne Dranowski, Aaron Lauda, and Andrew Manion.