Noncommutative geometry : a functorial approach / Igor V. Nikolaev.

Format:

Book

Author/Creator:

Nikolaev, Igor, 1961- author.

Series:

De Gruyter studies in mathematics ; Volume 66.

De Gruyter studies in mathematics ; Volume 66

Language:

English

Subjects (All):

Geometry, Algebraic.

Noncommutative differential geometry.

Number theory.

Physical Description:

1 online resource (xx, 380 pages) : illustrations

Edition:

Second edition.

Place of Publication:

Berlin, Germany : Walter de Gruyter GmbH, [2022]

Language Note:

In English.

Summary:

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.

Contents:

Frontmatter

Foreword

Foreword to the second edition

Introduction

Contents

Part I: Basics

1 Model examples

2 Categories and functors

3 C∗-algebras

Part II: Noncommutative invariants

4 Topology

5 Algebraic geometry

6 Number theory

7 Arithmetic topology

8 Quantum arithmetic

Part III: Brief survey of NCG

9 Finite geometries

10 Continuous geometries

11 Connes geometries

12 Index Theory

13 Jones polynomials

14 Quantum groups

15 Noncommutative algebraic geometry

16 Trends in noncommutative geometry

Bibliography

Index

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9783110788709

3-11-078870-5

OCLC:

1338021554