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On a formula for the spectral flow and its applications

✍ Scribed by Pierluigi Benevieri; Paolo Piccione

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
315 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi-Riemannian geodesic, and we compute its value in terms of the Maslov index.

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