On von Neumann spectral triples

Details On von Neumann spectral triples On von Neumann spectral triples

2000-12-22

arxiv.org/abs/math/0012233v4

Mathematics

K-Theory and Homology

This paper has been withdrawn by the authors

Scientific paper

We define the notion of von Neumann spectral triple and consider the associated index problem. We compute the analytic Chern-Connes character of such a von Neumann spectral triple and prove the corresponding local formula for its Hochschild class. This formula involves the Dixmier trace for $II_{\infty}$ von Neumann algebras. In the case of foliations, we identify this Dixmier trace with the corresponding measured Wodzicki residue.

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