Geometry and analysis seminar - Peter Hochs

Speaker: Peter Hochs, University of Adelaide, Australia

Title: An equivariant index for proper actions

Abstract: For a compact group G acting on a compact manifold M, the equivariant index of an elliptic differential operator D on M is the formal difference of the kernels of D and its adjoint, as representations of G. In the compact setting, equivariant index theory has applications to geometry and to representation theory of compact Lie groups. (The Borel-Weil theorem and Weyl’s character formula fit into this framework, for example.) This theory has been generalised to noncompact groups or manifolds, under the assumption that either G or M/G is compact. These two cases have so far been approached with very different techniques. In joint work with Yanli Song, we define and apply an equivariant index in cases where both G and M/G may be noncompact.