|Title||End-periodic $K$-homology and positive scalar curvature|
|Presenter||Michael Alexander Hallam (The University of Adelaide)|
|Author(s)||Michael Hallam, Mathai Varghese|
|Session||Category Theory, Algebraic Topology, K-Theory|
In this talk I will introduce a new variant of $K$-homology, called `end-periodic $K$-homology', that is tailored to a recent index theorem for end-periodic manifolds by Mrowka, Ruberman and Saveliev. The new $K$-homology groups elegantly encapsulate invariance properties of end-periodic rho invariants, and in fact are naturally isomorphic to the standard $K$-homology groups. The isomorphism preserves rho invariants, and so can be used to transfer results on positive scalar curvature for odd-dimensional manifolds to even-dimensional manifolds. This is joint work with Mathai Varghese.