I gave a talk in our seminar yesterday which arises from trying to understand the paper of Chang, Weinberger and Yu (Chang, Stanley, Shmuel Weinberger, and Guoliang Yu. “Positive Scalar Curvature and a New Index Theorem for Noncompact Manifolds,” 2013) where they use relative index theory in a non \(\pi-\pi\) situation to produce examples of manifolds with strange positive-scalar-curvature properties (e.g., a non-compact manifold which has an exhaustion by compact manifolds with boundary carrying nice positive-scalar-curvature metrics, but which itself carries no such metric).

I wanted to develop an approach to this kind of index theory that was more accessible (to me) and the talk was a report on my efforts in that direction. Here are the slides from that talk.