Spectral flow argument localizing an odd index pairing
Mathematical Physics
2018-05-29 v2 Functional Analysis
K-Theory and Homology
math.MP
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.
Cite
@article{arxiv.1802.04518,
title = {Spectral flow argument localizing an odd index pairing},
author = {Terry Loring and Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:1802.04518},
year = {2018}
}
Comments
minor corrections and improvements, to appear in Canadian Math Bull