Geometry & Topology Seminar: "Loop group and an index theory for infinite-dimensional manifolds"
Abstract: The Atiyah-Singer index theorem is one of monumental work in geometry and topology. This theorem states the coincidence between some differential geometrical quantity of closed manifolds can be topologically computed. There are various ramifications and generalizations. The overall goal of my research is to formulate and prove an infinite-dimensional version of this theorem. As a first step, I have been trying to establish it for some special cases, called "Hamiltonian loop group spaces''. In this talk, beginning with a brief exposition of the original index theorem, I will report the progress I have made so far.
Host: Yanli Song