Noncommutative Geometry : : A Functorial Approach / / Igor V. Nikolaev.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1
• VerfasserIn: Nikolaev, Igor V.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2022]; ©2022
• Year of Publication: 2022
• Edition: This is the revised second edition.
• Language: English
• Series: De Gruyter Studies in Mathematics , 66
• Physical Description: 1 online resource (XX, 380 p.)
• Other title: 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110788709; 9783110766820; 9783110993899; 9783110994810; 9783110993868; 9783110770445
• ISSN: 0179-0986
• DOI: 10.1515/9783110788709
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Igor V. Nikolaev.

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.