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 | ||||||||||||
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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 | ||||||||||||
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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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