Annular sl(3) web algebras

Rostislav Akhmechet (Columbia)

Abstract: Khovanov homology categorifies the Jones polynomial, the sl(2) specialization of an infinite family of knot invariants. I will discuss an sl(3) homology theory for links in the thickened annulus defined combinatorially via webs (certain trivalent graphs) and foams (certain singular surfaces viewed as cobordisms between webs). I will focus on the localization of this construction to tangles in the thickened annulus, which produces bimodules over certain algebras built from so-called "irreducible" webs in the annulus. A key technical step is an explicit description of irreducible annular webs, which extends earlier work of Khovanov and Kuperberg. This is joint work with Mikhail Khovanov and Melissa Zhang.