Geometry and Topology Seminar: A simplicial perspective for Lie groupoid representations and sheaves

Abstract: In this talk I will give a brief discussion of representations of Lie groupoids and the associated cohomology theories. From the Morita point of view, representations of Lie groupoids can be thought of as a kind of “vector bundle on a stack.” In this talk I will discuss how the simplicial perspective on representations can be used to generalize this notion to something more akin to a “sheaf of modules” over a stack. I will discuss a few applications/motivations for this generalization that relate to index theory and the construction of some new cohomological invariants for Lie groupoids.

This guest speaker will present via Zoom.