Algebra Seminar: Spin link homology

Abstract: For each simple Lie algebra, Reshetikhin-Turaev define a quantum invariant of knots/links in the 3-sphere with components colored by finite-dimensional representations. These invariants generalize the Jones polynomial, which corresponds to the case of sl(2) and the vector representation. One categorical level higher, Webster defines a link homology theory for each simple Lie algebra; this extends pioneering work of Khovanov(-Rozansky) that categorifies the Jones polynomial and its sl(n) variant. While sl(n) link homologies have
been widely studied and have found numerous applications in low-dimensional topology, essentially nothing is known about link homologies associated to other (non-Type A) Lie algebras, beyond their existence.

In this talk, we will present a new categorification of the spin-colored so(2n+1) link invariant, which arises from a novel involution on colored sl(2n) Khovanov-Rozansky homology. Our approach involves categorical representation theory, and highlights a subtle connection between link invariants in types A and B that is hidden at the decategorified level. Further, our construction is explicit and computable, thus should be amenable to topological applications. (This is joint work with Elijah Bodish and Ben Elias.)

Welcome to join on site or via Zoom link (Meeting ID: 645 5572 6999, please contact the organizer for passcode)

This is a seminar in our algebra seminar series.