The nilpotent cone for sl2 and annular link homology

Abstract: In this talk I will discuss an equivalence of categories relating SL(2)-equivariant vector bundles on the nilpotent cone for sl(2) and the annular Bar-Natan category (this latter category appears in the context of Khovanov homology for links in a thickened annulus). Indeed, both categories admit a diagrammatic description in terms of the same "dotted" Temperley-Lieb diagrammatics, as I will explain. Under this equivalence, Bezrukavnikov's quasi-exceptional collection on the nilcone (in the SL2 case) has an elegant description in terms of some special annular links. In recent joint work with Dave Rose and Paul Wedrich, we constructed a very special Ind-object in the annular Bar-Natan category which is a categorical analogue of a "Kirby element" from quantum topology; I will conclude by sketching a neat "BGG resolution" afforded by our categorified Kirby element. This is based on joint work with Rose and Wedrich.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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