KK -theory and spectral flow in von Neumann algebras

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We present a definition of spectral flow for any norm closed ideal J in any von Neumann algebra N. Given a path of selfadjoint operators in N which are invertible in N/J, the spectral flow produces a class in Ko (J).
Given a semifinite spectral triple (A, H, D) relative to (N, t) with A separable, we construct a class [D] ¿ KK1 (A, K(N)). For a unitary u ¿ A, the von Neumann spectral flow between D and u*Du is equal to the Kasparov product [u] A[D], and is simply related to the numerical spectral flow, and a refined C* -spectral flow.
Original languageEnglish
JournalJournal of K-Theory
Volume10
Issue number2
Pages (from-to)241-277
ISSN1865-2433
DOIs
Publication statusPublished - 2012

ID: 45182032