Spectral flow argument localizing an odd index pairing

2018/02/13 by Loring, Terry, Schulz-Baldes, Hermann · 3 citations
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1802.04518

Abstract

An odd Fredholm module for a given invertible operator on a Hilbert space is specified by an unbounded so-called Dirac operator with compact resolvent and bounded commutator with the given invertible. Associated to this is an index pairing in terms of a Fredholm operator with Noether index. Here it is shown by a spectral flow argument how this index can be calculated as the signature of a finite dimensional matrix called the spectral localizer.

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