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June 2016 Index map, σ-connections, and Connes–Chern character in the setting of twisted spectral triples
Raphaël Ponge, Hang Wang
Kyoto J. Math. 56(2): 347-399 (June 2016). DOI: 10.1215/21562261-3478907

Abstract

Twisted spectral triples are a twisting of the notion of spectral triples aimed at dealing with some type III geometric situations. In the first part of the article, we give a geometric construction of the index map of a twisted spectral triple in terms of σ-connections on finitely generated projective modules. This clarifies the analogy with the indices of Dirac operators with coefficients in vector bundles. In the second part, we give a direct construction of the Connes–Chern character of a twisted spectral triple, in both the invertible and the noninvertible cases. Combining these two parts we obtain an analogue of the Atiyah–Singer index formula for twisted spectral triples.

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Raphaël Ponge. Hang Wang. "Index map, σ-connections, and Connes–Chern character in the setting of twisted spectral triples." Kyoto J. Math. 56 (2) 347 - 399, June 2016. https://doi.org/10.1215/21562261-3478907

Information

Received: 21 February 2015; Accepted: 24 March 2015; Published: June 2016
First available in Project Euclid: 10 May 2016

zbMATH: 1361.46055
MathSciNet: MR3500845
Digital Object Identifier: 10.1215/21562261-3478907

Subjects:
Primary: 46L87 , 58B34
Secondary: 19D55 , 58J20

Keywords: cyclic cohomology , Index theory , noncommutative geometry , twisted spectral triples

Rights: Copyright © 2016 Kyoto University

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Vol.56 • No. 2 • June 2016
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