Spectral flow for nonunital spectral triples

Authors

A L. Carey, University of Wollongong
V Gayral, Universite Reims Champagne-ArdenneFollow
J Phillips, University of Victoria
A Rennie, University of WollongongFollow
F A. Sukochev, University of New South Wales

RIS ID

102390

Publication Details

Carey, A. L., Gayral, V., Phillips, J., Rennie, A. & Sukochev, F. A. (2015). Spectral Flow for Nonunital Spectral Triples. Canadian Journal of Mathematics, 67 (4), 759-794.

Abstract

We 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 satisfies 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.