Spectral flow, index and the signature operator

Spectral flow, index and the signature operator

We relate the spectral flow to the index for paths of selfadjoint Breuer-Fredholm operators affiliated to a semifinite von Neumann algebra, generalizing results of Robbin-Salamon and Pushnitski. Then we prove the vanishing of the von Neumann spectral flow for the tangential signature operator of a f...

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Veröffentlicht in:arXiv.org 2009-11
Hauptverfasser: Azzali, Sara, Wahl, Charlotte
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Manifolds
Operators (mathematics)
Spectra
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description We relate the spectral flow to the index for paths of selfadjoint Breuer-Fredholm operators affiliated to a semifinite von Neumann algebra, generalizing results of Robbin-Salamon and Pushnitski. Then we prove the vanishing of the von Neumann spectral flow for the tangential signature operator of a foliated manifold when the metric is varied. We conclude that the tangential signature of a foliated manifold with boundary does not depend on the metric. In the Appendix we reconsider integral formulas for the spectral flow of paths of bounded operators.
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subjects Manifolds
Operators (mathematics)
Spectra
title Spectral flow, index and the signature operator
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