Journal of the Ramanujan Mathematical Society

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On the Noncommutative Spectral Flow


Affiliations
1 Nieders¨achsische Landesbibliothek, Gottfried Wilhelm Leibniz Bibliothek, Waterloostr. 8, 30169 Hannover, Germany
     

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We define and study the noncommutative spectral flow for paths of regular selfadjoint Fredholm operators on a Hilbert C ∗-module. We give an axiomatic description and discuss some applications. One of them is the definition of a noncommutative Maslov index for paths of Lagrangians, which appears in a splitting formula for the spectral flow. Analogously we study the spectral flow for odd operators on a Z/2-graded module.
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  • On the Noncommutative Spectral Flow

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Authors

Charlotte Wahl
Nieders¨achsische Landesbibliothek, Gottfried Wilhelm Leibniz Bibliothek, Waterloostr. 8, 30169 Hannover, Germany

Abstract


We define and study the noncommutative spectral flow for paths of regular selfadjoint Fredholm operators on a Hilbert C ∗-module. We give an axiomatic description and discuss some applications. One of them is the definition of a noncommutative Maslov index for paths of Lagrangians, which appears in a splitting formula for the spectral flow. Analogously we study the spectral flow for odd operators on a Z/2-graded module.