The Joint Spectral Flow and Localization of the Indices of Elliptic Operators

Abstract

We introduce the notion of the joint spectral flow, which is a generalization of the spectral flow, by using Segal's model of the connective $K$-theory spectrum. We apply it for some localization results of indices motivated by Witten's deformation of Dirac operators and rephrase some analytic techniques in terms of topology.

35 pages

References in corpus (2)

• A local global principle for regular operators in Hilbert C*-modules
• On the noncommutative spectral flow

Cited by in corpus (3)

• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Spectral convergence in geometric quantization -- the case of non-singular Langrangian fibrations
• The geometric quantizations and the measured Gromov-Hausdorff convergences