The Local Index Formula in Semifinite von Neumann Algebras I: Spectral Flow

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We generalise the local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \A of a general semifinite von Neumann algebra. In this setting it gives a formula for spectral flow along a path joining an unbounded self adjoint Breuer-Fredholm operator, affiliated to the von Neumann algebra, to a unitarily equivalent operator. Our proof is novel even in the setting of the original theorem and relies on the introduction of a function valued cocycle which is `almost' a (b,B)-cocycle in the cyclic cohomology of \A.
53 pages, to appear in Advances in Mathematics

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Operator Algebras, K-Theory and Homology

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http://salesiana.dossiersoluciones.com/handle/123456789/73062

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411019
 http://arxiv.org/abs/math/0411019

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arXiv