The spectral localizer for semifinite spectral triples

2020/04/27 by Schulz-Baldes, Hermann, Stoiber, Tom · 3 citations
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2004.13092

Abstract

The notion of spectral localizer is extended to pairings with semifinite spectral triples. By a spectral flow argument, any semifinite index pairing is shown to be equal to the signature of the spectral localizer. As an application, a formula for the weak invariants of topological insulators is derived. This provides a new approach to their numerical evaluation.

Cited by

• Spectral localizers in KK-theory
• Explicit equivalence between the spectral localizer and local Chern and winding markers
• The odd spectral localiser via asymptotic morphisms and quasi-projections

Related

• Detecting local topology with the spectral localizer
• The spectral localizer for even index pairings
• Finite volume calculation of K-theory invariants
• Explicit equivalence between the spectral localizer and local Chern and winding markers
• The Loring--Schulz-Baldes Spectral Localizer Revisited