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Classification of spin structures on the noncommutative n-torus

Venselaar, Jan Jitse (2013) Classification of spin structures on the noncommutative n-torus. Journal of Noncommutative Geometry, 7 (3). pp. 787-816. ISSN 1661-6952. doi:10.4171/JNCG/135. https://resolver.caltech.edu/CaltechAUTHORS:20131220-141257532

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Abstract

We classify spin structures on the noncommutative torus and find that the noncommutative n-torus has 2^n spin structures corresponding to isospectral deformations of spin structures on the commutative n-torus. For n≥4 the classification depends on Connes’ spin manifold theorem. In addition, we study unitary equivalences of these spin structures.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1003.5156arXivDiscussion Paper
http://dx.doi.org/10.4171/JNCG/135 DOIArticle
http://www.ems-ph.org/journals/show_abstract.php?issn=1661-6952&vol=7&iss=3&rank=7PublisherArticle
Additional Information:© 2013 European Mathematical Society. Received April 19, 2011; revised July 25, 2011. The author thanks Gunther Cornelissen for discussions and encouragement, and the referee for pertinent remarks.
Subject Keywords:Spectral geometry; noncommutative geometry; real spectral triples
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR3108696
Issue or Number:3
Classification Code:Mathematics Subject Classification (2010): 58B34; 46L87
DOI:10.4171/JNCG/135
Record Number:CaltechAUTHORS:20131220-141257532
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20131220-141257532
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43123
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:23 Dec 2013 19:47
Last Modified:10 Nov 2021 16:33

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