Spectral Flow for Nonunital Spectral Triples

Carey, A. L. ; Gayral, V. ; Phillips, J. ; Rennie, A. ; Sukochev, F. A.

Canadian journal of mathematics, Tome 67 (2015) no. 4, pp. 759-794

Résumé

We prove two results about nonunital index theory left open in a previous paper. Thefirst 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.

Détail

DOI : 10.4153/CJM-2014-042-x

Mots-clés : 46H30, spectral triple, spectral flow, local index theorem

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