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An Introduction to Noncommutative Ge...

Várilly, Joseph C.,

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An Introduction to Noncommutative Geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	An Introduction to Noncommutative Geometry/ Joseph C. Várilly
Author:	Várilly, Joseph C.,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2006,
Description:	1 online resource (121 pages)
Subject:	Differential & Riemannian geometry -
Online resource:	https://doi.org/10.4171/024
Online resource:	https://www.ems-ph.org/img/books/varilly_mini.jpg
ISBN:	9783037195246

An Introduction to Noncommutative Geometry
Várilly, Joseph C.,

An Introduction to Noncommutative Geometry[electronic resource] /Joseph C. Várilly - Zuerich, Switzerland :European Mathematical Society Publishing House,2006 - 1 online resource (121 pages) - EMS Series of Lectures in Mathematics (ELM) ;2523-5176.

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

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 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. 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.

ISBN: 9783037195246

Standard No.: 10.4171/024doiSubjects--Topical Terms:

3480810
Differential & Riemannian geometry

An Introduction to Noncommutative Geometry
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520 $a 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 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. 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.
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