The spectral localizer for even index pairings
Mathematical Physics
2018-02-14 v1 Functional Analysis
K-Theory and Homology
math.MP
Abstract
Even index pairings are integer-valued homotopy invariants combining an even Fredholm module with a -class specified by a projection. Numerous classical examples are known from differential and non-commutative geometry and physics. Here it is shown how to construct a finite dimensional selfadjoint and invertible matrix, called the spectral localizer, such that half its signature is equal to the even index pairing. This makes the invariant numerically accessible. The index-theoretic proof heavily uses fuzzy spheres.
Keywords
Cite
@article{arxiv.1802.04517,
title = {The spectral localizer for even index pairings},
author = {Terry Loring and Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:1802.04517},
year = {2018}
}