Jump to ContentJump to Main Navigation
Show Summary Details

Nikolaev, Igor V.

Noncommutative Geometry

A Functorial Approach

Series:De Gruyter Studies in Mathematics 66

    99,95 € / $114.99 / £91.00*

    Publication Date:
    November 2017
    See all formats and pricing


    • 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.

    Part I: Basics
    Model examples
    Categories and functors

    Part II: Noncommutative invariants
    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


    24.0 x 17.0 cm
    xiii, 263 pages
    40 Fig. 2 Tables
    Type of Publication:

    request permissions

    More ...

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


    "The book is a good survey of noncommutative geometry, and is an excellent starting point for doing good research in the field. Each section of the book ends with a list of references for going deeply into each subject, and so this book gives a framework for the field of noncommutative geometry." Zentralblatt für Mathematik

    "In any case, it is true with a vengeance that NCG is a big and important subject, and the book we are looking at here, with its subtitle of "A functorial approach" is doubtless a very valuable contribution on any number of counts, not the least of which being that the more functorial we get, the more generality we reap, and the clearer the overarching structure becomes. [...] In point of fact, the book under review is the first book on NCG to take a functorial approach as its Leitmotiv, and that is in itself a very solid contribution, pedagogically and mathematically." MAA Reviews

    Comments (0)

    Please log in or register to comment.
    Log in