Geometry and Topology Seminar: "Coarse Geometry and Callias Quantization"

Abstract: I will report on some recent joint work with Peter Hochs and Mathai Varghese at the University of Adelaide on index theory of a class of elliptic operators on non-compact manifolds that are invertible outside of a small set, with respect to some group of symmetries on the manifold. The index we study takes values in the maximal C*-algebra of this group. Our approach uses a maximal version of the localised Roe algebra. The advantage of using the maximal version of the index is that it admits a natural trace defined by integration. As a motivating application, I will mention a version of Guillemin and Sternberg’s quantization commutes with reduction principle for equivariant indices of spin-c Callias-type operators.

Host: Michael Landry