Finite volume calculation of K-theory invariants

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Schulz-Baldes H, Loring T
Zeitschrift: New York Journal of Mathematics
Jahr der Veröffentlichung: 2017
Band: 22
Seitenbereich: 1111 - 1140
ISSN: 1076-9803


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.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Schulz-Baldes, Hermann Prof. Dr.
Professur für Mathematik (Mathematische Physik)


Einrichtungen weiterer Autorinnen und Autoren

University of New Mexico


Zitierweisen

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.

BibTeX: 

Zuletzt aktualisiert 2018-24-07 um 10:38