Noncommutative Geometry: A Functorial Approach

Igor V. Nikolaev

Published by De Gruyter 2022

Noncommutative Geometry

A Functorial Approach

Igor V. Nikolaev

Volume 66 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110788709

Overview
Contents

About this book

Noncommutative geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. This book covers the key concepts of noncommutative geometry and its applications in topology, algebraic geometry, and number theory. Our presentation is accessible to the graduate students as well as nonexperts in the field. The second edition includes two new chapters on arithmetic topology and quantum arithmetic.

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

Author information

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

Topics

Frontmatter Publicly Available Download PDF	I
Foreword Publicly Available Download PDF	VII
Foreword to the second edition Publicly Available Download PDF	IX
Introduction Publicly Available Download PDF	XI
Contents Publicly Available Download PDF	XIII
Part I: Basics
1 Model examples Requires Authentication Unlicensed Licensed Download PDF	1
2 Categories and functors Requires Authentication Unlicensed Licensed Download PDF	23
3 C∗-algebras Requires Authentication Unlicensed Licensed Download PDF	31
Part II: Noncommutative invariants
4 Topology Requires Authentication Unlicensed Licensed Download PDF	53
5 Algebraic geometry Requires Authentication Unlicensed Licensed Download PDF	103
6 Number theory Requires Authentication Unlicensed Licensed Download PDF	143
7 Arithmetic topology Requires Authentication Unlicensed Licensed Download PDF	207
8 Quantum arithmetic Requires Authentication Unlicensed Licensed Download PDF	249
Part III: Brief survey of NCG
9 Finite geometries Requires Authentication Unlicensed Licensed Download PDF	303
10 Continuous geometries Requires Authentication Unlicensed Licensed Download PDF	309
11 Connes geometries Requires Authentication Unlicensed Licensed Download PDF	313
12 Index Theory Requires Authentication Unlicensed Licensed Download PDF	325
13 Jones polynomials Requires Authentication Unlicensed Licensed Download PDF	341
14 Quantum groups Requires Authentication Unlicensed Licensed Download PDF	347
15 Noncommutative algebraic geometry Requires Authentication Unlicensed Licensed Download PDF	353
16 Trends in noncommutative geometry Requires Authentication Unlicensed Licensed Download PDF	359
Bibliography Requires Authentication Unlicensed Licensed Download PDF	365
Index Requires Authentication Unlicensed Licensed Download PDF	375

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: This is the revised second edition.
Audience: Graduate students and researchers in noncommutative and algebraic geometry, topology, and number theory.
Pages
- Front matter: 20
- Main content: 380
Illustrations
- Illustrations: 60
Keywords: Algebraic geometry; number theory; continuous geometries; topology; noncommutative algebraic geometry; quantum Arithmetic.

eBook

Published: July 18, 2022
ISBN: 9783110788709

Hardcover

Published: July 18, 2022
ISBN: 9783110788600