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Symmetry, Integrability and Geometry: Methods and Applications, 2014, Volume 10, 077, 25 pp.
DOI: https://doi.org/10.3842/SIGMA.2014.077
(Mi sigma942)
 

This article is cited in 10 scientific papers (total in 10 papers)

Quantitative $K$-Theory Related to Spin Chern Numbers

Terry A. Loring

Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA
References:
Abstract: 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.
Keywords: $K$-theory; $C^{*}$-algebras; matrices.
Received: January 15, 2014; in final form July 13, 2014; Published online July 19, 2014
Bibliographic databases:
Document Type: Article
MSC: 19M05; 46L60; 46L80
Language: English
Citation: Terry A. Loring, “Quantitative $K$-Theory Related to Spin Chern Numbers”, SIGMA, 10 (2014), 077, 25 pp.
Citation in format AMSBIB
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\paper Quantitative $K$-Theory Related to Spin Chern Numbers
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\totalpages 25
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
     
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