Quantitative K-Theory Related to Spin Chern Numbers

We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, that of general unitary matrices and that of self-dual matrices, with an emphasis on quantitative results. We determine wh...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2014
1. Verfasser: Loring, T.A.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2014
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146609
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Quantitative K-Theory Related to Spin Chern Numbers / T.A. Loring // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 22 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Beschreibung
Zusammenfassung:We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, that of general unitary matrices and that of self-dual matrices, with an emphasis on quantitative results. We determine which values of the norm of the commutator guarantee that the indices are defined, where they are equal, and what quantitative results on the distance to a pair with a different index are possible. We validate a method of computing spin Chern numbers that was developed with Hastings and only conjectured to be correct. Specifically, the Pfaffian-Bott index can be computed by the ''log method'' for commutator norms up to a specific constant.
ISSN:1815-0659