Dirac operators on noncommutative principal torus bundles

Spectral triples over noncommutative principal \(\T^n\)-bundles are studied, extending recent results about the noncommutative geometry of principal U(1)-bundles. We relate the noncommutative geometry of the total space of the bundle with the geometry of the base space. Moreover, strong connections...

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Bibliographic Details
Published inarXiv.org
Main Authors Zucca, Alessandro, Dabrowski, Ludwik
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.08.2013
Subjects
Bundles
Bundling
Deformation
Geometry
Operators (mathematics)
Toruses
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Summary:Spectral triples over noncommutative principal \(\T^n\)-bundles are studied, extending recent results about the noncommutative geometry of principal U(1)-bundles. We relate the noncommutative geometry of the total space of the bundle with the geometry of the base space. Moreover, strong connections are used to build new Dirac operators. We discuss as a particular case the commutative case, the noncommutative tori and theta deformed manifolds.
ISSN:2331-8422