Tag Archives: K-homology

“Operator K-theory” has appeared on AMS Open Math Notes

My final Penn State course (Spring 2017) was about K-theory and operator algebras – the connection between these two has been central to my mathematical life.  I wrote up lecture notes for this course, as has become usual for me.  I’m pleased to report that these have now appeared on the AMS Open Math Notes page.

The American Mathematical Society hosts AMS Open Math Notes,  which is “a repository of freely downloadable mathematical works in progress hosted by the AMS as a service to researchers, teachers and students.”

The Open Math Notes homepage continues  “These draft works include course notes, textbooks, and research expositions in progress. They have not been published elsewhere, and, as works in progress, are subject to significant revision.  Visitors are encouraged to download and use these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.”



Higher index theory with change of fundamental group

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.