Geometry and Topology Seminar: "Annular link Floer homology and gl(1|1)"

Abstract: In earlier work by Ellis, Petkova, and Vertesi, tangle Floer bimodules (a combinatorial generalization of link Floer homology) are shown to decategorify to the Reshetikhin–Turaev invariants arising in the representation theory of gl(1|1). In this talk, we describe how this can give rise to a gl(1|1) action on annular link Floer homology, viewed as the Hochschild homology—or horizontal trace—of a tangle Floer bimodule. The gl(1|1) action turns out to be closely related to a known basepoint action in Floer theory. This is based on joint work in progress with Andy Manion and Ina Petkova.

Host: Michael Landry