On the noncommutative spectral flow

Details On the noncommutative spectral flow On the noncommutative spectral flow

2006-02-07

arxiv.org/abs/math/0602110v4

J. Ramanujan Math. Soc. 22 (2), 2007, pp. 135-187

Mathematics

Operator Algebras

48 pages, 1 figure; statement of Prop. 3.7 generalized, discussion of references updated, minor changes

Scientific paper

We define and study the noncommutative spectral flow for paths of regular selfadjoint Fredholm operators on a countably generated 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 graded module.

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