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OverviewNoncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras, and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples. This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the condiditons on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples. Full Product DetailsAuthor: Joseph C. VarillyPublisher: European Mathematical Society Imprint: European Mathematical Society Weight: 0.250kg ISBN: 9783037190241ISBN 10: 3037190248 Pages: 121 Publication Date: 01 January 2006 Audience: College/higher education , Undergraduate Format: Paperback Publisher's Status: Active Availability: Awaiting stock  The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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