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Noncommutative geometry: a functorial approach

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This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with  Read more...

Abstract: This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field.--Provided by publisher

Author(s): Nikolaev Igor V.
Series: De Gruyter studies in mathematics 66
Publisher: de Gruyter
Year: 2017

Language: English
Pages: 263
Tags: Noncommutative differential geometry.;Geometry, Algebraic.;Number theory.

Content: Introduction --
Basics --
Model examples --
Categories and functors --
C-algebras --
Noncommutative invariants --
Topology --
Algebraic geometry --
Number theory --
Brief survey of NCG --
Finite geometries --
Continuous geometries --
Connes geometries --
Index theory --
Jones polynomials --
Quantum groups --
Noncommutative algebraic geometry --
Trends in noncommutative geometry.