Spectral Flow for Nonunital Spectral Triples

Abstract

AbstractWe prove two results about nonunital index theory left open in a previous paper. The first is that the spectral triple arising from an action of the reals on a C*-algebra with invariant trace satisûes the hypotheses of the nonunital local index formula. The second result concerns the meaning of spectral flow in the nonunital case. For the special case of paths arising from the odd index pairing for smooth spectral triples in the nonunital setting, we are able to connect with earlier approaches to the analytic definition of spectral flow