The spectral localizer for even index pairings

2018/02/13 by Loring, Terry, Schulz-Baldes, Hermann · 9 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.1802.04517

Abstract

Even index pairings are integer-valued homotopy invariants combining an even Fredholm module with a K₀-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.

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