Classification and equivalences of noncommutative tori and quantum lens spaces

J.J. Venselaar

Research output: ThesisDoctoral thesis 1 (Research UU / Graduation UU)

Abstract

In noncommutative geometry, one studies abstract spaces through their, possibly noncommutative, algebras of continuous functions. Through these function algebras, and certain operators interacting with them, one can derive much geometrical information of the underlying space, even though this space does not exist as a classical topological space if the algebra is noncommutative. In this thesis the classification of certain geometrical structures, spin structures, is extended to several kinds of noncommutative spaces: noncommutative tori and quantum lens spaces. It is found that this classification yields very similar results to the classical geometrical classification, even though the methods are completely different. Also, equivalences between these spaces and spinstructures are considered. It is proven that a certain proposed equivalence, Morita equivalence of spectral triples, is really an equivalence in the case of noncommutative tori. In general, it is not known when a Morita equivalence of spectral triples is really an equivalence relation.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Utrecht University
Supervisors/Advisors
  • Cornelissen, Gunther, Primary supervisor
Award date28 Aug 2012
Publisher
Print ISBNs978-90-393-5829-0
Publication statusPublished - 28 Aug 2012

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