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Noncommutative Geometry
A Functorial Approach
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Igor V. Nikolaev
Language:
English
Published/Copyright:
2022
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 / Editor information
Igor V. Nikolaev, St. John’s University, USA.
Topics
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Frontmatter
I -
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Foreword
VII -
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Foreword to the second edition
IX -
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Introduction
XI -
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Contents
XIII - Part I: Basics
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1 Model examples
1 -
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2 Categories and functors
23 -
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3 C∗-algebras
31 - Part II: Noncommutative invariants
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4 Topology
53 -
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5 Algebraic geometry
103 -
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6 Number theory
143 -
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7 Arithmetic topology
207 -
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8 Quantum arithmetic
249 - Part III: Brief survey of NCG
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9 Finite geometries
303 -
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10 Continuous geometries
309 -
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11 Connes geometries
313 -
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12 Index Theory
325 -
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13 Jones polynomials
341 -
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14 Quantum groups
347 -
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15 Noncommutative algebraic geometry
353 -
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16 Trends in noncommutative geometry
359 -
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Bibliography
365 -
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Index
375
Publishing information
Pages and Images/Illustrations in book
eBook published on:
July 18, 2022
eBook ISBN:
9783110788709
Hardcover published on:
July 18, 2022
Hardcover ISBN:
9783110788600
Edition:
This is the revised second edition.
Pages and Images/Illustrations in book
Front matter:
20
Main content:
380
Illustrations:
60
Keywords for this book
Algebraic geometry; number theory; continuous geometries; topology; noncommutative algebraic geometry; quantum Arithmetic.
Audience(s) for this book
Graduate students and researchers in noncommutative and algebraic geometry, topology, and number theory.
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
