TY  - BOOK
AU  - Várilly,Joseph C.
AU  - Várilly,Joseph C.
TI  - An Introduction to Noncommutative Geometry
T2  - EMS Series of Lectures in Mathematics (ELM)
SN  - 9783037195246
PY  - 2006///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Differential & Riemannian geometry
KW  - bicssc
KW  - Relativistic quantum mechanics & quantum field theory
KW  - Global analysis, analysis on manifolds
KW  - msc
KW  - Functional analysis
KW  - Quantum theory
N1  - Restricted to subscribers
N2  - 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
UR  - https://doi.org/10.4171/024
UR  - http://www.ems-ph.org/img/books/varilly_mini.jpg
ER  -