Spectral flow, index and the signature operator

Details Spectral flow, index and the signature operator Spectral flow, index and the signature operator

2009-11-15

arxiv.org/abs/0911.2862v1

J. Top. Anal. 3 (2011), no. 1, pp. 37-67

Mathematics

Differential Geometry

23 pages

Scientific paper

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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