An introduction to noncommutative geometry pdf epub mobi txt 电子书 下载 2024


An introduction to noncommutative geometry

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Joseph C. Várilly
European Mathematical Society
2006-6-15
113
332.20元
EMS Series of Lectures in Mathematics
9783037190241

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发表于2024-11-11

An introduction to noncommutative geometry epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

An introduction to noncommutative geometry epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

An introduction to noncommutative geometry pdf epub mobi txt 电子书 下载 2024



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Noncommutative 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 conditions 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. The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

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