On a formula for the spectral flow and its applications | Zendy

Benevieri Pierluigi | Zendy; Piccione Paolo | Zendy

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On a formula for the spectral flow and its applications

Author(s) -

Benevieri Pierluigi,

Piccione Paolo

Publication year - 2010

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200710232

Subject(s) - mathematics , linear subspace , hilbert space , flow (mathematics) , pure mathematics , geodesic , path (computing) , subspace topology , mathematical analysis , geometry , computer science , programming language

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 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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