Spectral Flow for Nonunital Spectral Triples

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 mean...

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Bibliographic Details
Published in:Canadian journal of mathematics 2015-08, Vol.67 (4), p.759-794
Main Authors: Carey, A. L., Gayral, V., Phillips, J., Rennie, A., Sukochev, F. A.
Format: Article
Language:English
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Summary: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.
ISSN:0008-414X
1496-4279
DOI:10.4153/CJM-2014-042-x