The spectral localizer for even index pairings

Loring TA, Schulz-Baldes H (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Journal of Noncommutative Geometry European Mathematical Society

Book Volume: 14

Pages Range: 1-23

Journal Issue: 1

DOI: 10.4171/JNCG/357

Abstract

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

Authors with CRIS profile

Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

University of New Mexico (UNM) / Universidad de Nuevo México US United States (USA) (US)

How to cite

APA:

Loring, T.A., & Schulz-Baldes, H. (2020). The spectral localizer for even index pairings. Journal of Noncommutative Geometry, 14(1), 1-23. https://dx.doi.org/10.4171/JNCG/357

MLA:

Loring, Terry A., and Hermann Schulz-Baldes. "The spectral localizer for even index pairings." Journal of Noncommutative Geometry 14.1 (2020): 1-23.

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