Geometry and Topology Seminar: Proper cocompact Kervaire semi-characteristics in KK-theory

Abstract: In this talk, I will introduce my recent work on the Kervaire semi-characteristic and its related vanishing theorem in the case of noncompact manifolds admitting proper cocompact Lie group actions. This study generalizes Atiyah and Singer's mod 2 index using Kasparov's KK-groups and the Baum-Connes assembly map. Also, it is an application of the proper cocompact elliptic theory developed by Bunke, Mathai, and Zhang in 2008 and the proper cocompact Hodge theorem proved by Tang, Yao, and Zhang in 2013.

Host: Parker Evans