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arXiv · 0911.2862

Spectral flow, index and the signature operator

Sara Azzali·Charlotte Wahl
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Abstract

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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Sara Azzali, Charlotte Wahl. 2009-11-15. Spectral flow, index and the signature operator. https://arxiv.org/abs/0911.2862

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