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The local index formula in semifinite Von Neumann algebras I: Spectral flow

Carey, Alan; Phillips, John; Rennie, Adam Charles; Sukochev, Fedor A


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...[Show more]

CollectionsANU Research Publications
Date published: 2006
Type: Journal article
Source: Advances in Mathematics
DOI: 10.1016/j.aim.2005.03.011


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