AG Mathematische Physik

The Cayley transform and K-theory

Dr. Chris Bourne (RIKEN, Tohoku)

Abstract:
The Cayley transform gives a passage between unitary operators and self-adjoint (unbounded) operators on a Hilbert space. I will review this construction and its generalisation to Hilbert C*-modules, where the Cayley transform furnishes an isomorphism on (odd) K-theory. Next, we consider a graded analogue of these results and their application to bulk and boundary invariants of topological phases. This is joint work with Johannes Kellendonk and Adam Rennie.