On the noncommutative spectral flow

Abstract

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.

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

References in corpus (3)

• Relative pairing in cyclic cohomology and divisor flows
• Homological index formulas for elliptic operators over C*-algebras
• A new topology on the space of unbounded selfadjoint operators and the spectral flow

Cited by in corpus (6)

• Higher rho-invariants and the surgery structure set
• Spectral sections, twisted rho invariants and positive scalar curvature
• The Joint Spectral Flow and Localization of the Indices of Elliptic Operators
• Index Theory of Chiral Unitaries and Split-Step Quantum Walks
• Generalised Dirac-Schrödinger operators and the Callias Theorem
• Dirac-Schrödinger operators, index theory, and spectral flow