Finite volume calculation of K-theory invariants

Schulz-Baldes H, Loring T (2017)

Publication Type: Journal article

Publication year: 2017

Journal

New York Journal of Mathematics Electronic Journals Project

Book Volume: 22

Pages Range: 1111 - 1140

Abstract

Odd index pairings of K1-group elements with Fredholm modules are of relevance in index theory, differential geometry and applications such as to topological insulators. For the concrete setting of operators on a Hilbert space over a lattice, it is shown how to calculate the resulting index as the signature of a suitably constructed finite-dimensional matrix, more precisely the finite volume restriction of what we call the spectral localizer. In presence of real symmetries, secondary ℤ2-invariants can be obtained as the sign of the Pfaffian of the spectral localizer. These results reconcile two complementary approaches to invariants of topological insulators.

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:

Schulz-Baldes, H., & Loring, T. (2017). Finite volume calculation of K-theory invariants. New York Journal of Mathematics, 22, 1111 - 1140.

MLA:

Schulz-Baldes, Hermann, and Terry Loring. "Finite volume calculation of K-theory invariants." New York Journal of Mathematics 22 (2017): 1111 - 1140.

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