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Nikolaev, Igor V.

Noncommutative Geometry

A Functorial Approach

Series:De Gruyter Studies in Mathematics 66

    99,95 € / $114.99 / £81.99*

    Hardcover
    Publication Date:
    November 2017
    ISBN
    978-3-11-054317-9
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    Overview

    • An authoritative introductory treatment of noncommutative geometry.
    • A novel approach using functors is presented in detail.
    • Covers applications of the theory in topology, algebraic geometry, and number theory.

    Aims and Scope

    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.

    Contents
    Part I: Basics
    Model examples
    Categories and functors
    C∗-algebras

    Part II: Noncommutative invariants
    Topology
    Algebraic geometry
    Number theory

    Part III: Brief survey of NCG
    Finite geometries
    Continuous geometries
    Connes geometries
    Index theory
    Jones polynomials
    Quantum groups
    Noncommutative algebraic geometry
    Trends in noncommutative geometry

    Details

    24.0 x 17.0 cm
    xiii, 263 pages
    40 Fig. 2 Tables
    Language:
    English
    Type of Publication:
    Monograph
    Keyword(s):

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    Igor V. Nikolaev, St. John’s University, USA.

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