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Basic Noncommutative Geometry: Second Edition
 
Masoud Khalkhali University of Western Ontario, London, Ontario, Canada
A publication of European Mathematical Society
Basic Noncommutative Geometry
Softcover ISBN:  978-3-03719-128-6
Product Code:  EMSSERLEC/10.R
List Price: $48.00
AMS Member Price: $38.40
Please note AMS points can not be used for this product
Basic Noncommutative Geometry
Click above image for expanded view
Basic Noncommutative Geometry: Second Edition
Masoud Khalkhali University of Western Ontario, London, Ontario, Canada
A publication of European Mathematical Society
Softcover ISBN:  978-3-03719-128-6
Product Code:  EMSSERLEC/10.R
List Price: $48.00
AMS Member Price: $38.40
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Series of Lectures in Mathematics
    Volume: 102013; 257 pp
    MSC: Primary 58;

    This text provides an introduction to noncommutative geometry and some of its applications. It can be used either as a textbook for a graduate course or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject.

    One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful.

    Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes–Chern characters in \(K\)-theory and \(K\)-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well.

    Two new sections have been added to the second edition: the first new section concerns the Gauss–Bonnet theorem and the definition and computation of the scalar curvature of the curved noncommutative two torus, and the second new section is a brief introduction to Hopf cyclic cohomology. The bibliography has been extended and some new examples are presented.

    A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

    Readership

    Graduate students and research mathematicians interested in mathematics and theoretical physics.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 102013; 257 pp
MSC: Primary 58;

This text provides an introduction to noncommutative geometry and some of its applications. It can be used either as a textbook for a graduate course or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject.

One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful.

Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes–Chern characters in \(K\)-theory and \(K\)-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well.

Two new sections have been added to the second edition: the first new section concerns the Gauss–Bonnet theorem and the definition and computation of the scalar curvature of the curved noncommutative two torus, and the second new section is a brief introduction to Hopf cyclic cohomology. The bibliography has been extended and some new examples are presented.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in mathematics and theoretical physics.

Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.