1.

Record Nr.

UNINA9910539691103321

Autore

Nikolaev Igor <1961->

Titolo

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

Pubbl/distr/stampa

Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2017

©2017

ISBN

3-11-054348-6

Descrizione fisica

1 online resource (266 pages) : illustrations

Collana

De Gruyter Studies in Mathematics, , 0179-0986 ; ; Volume 66

Classificazione

SK 240

Disciplina

516.3/5

Soggetti

Noncommutative differential geometry

Geometry, Algebraic

Number theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Frontmatter -- Preface -- Contents -- Introduction -- 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 -- Part III: Brief survey of NCG -- 7. Finite geometries -- 8. Continuous geometries -- 9. Connes geometries -- 10. Index theory -- 11. Jones polynomials -- 12. Quantum groups -- 13. Noncommutative algebraic geometry -- 14. Trends in noncommutative geometry -- References -- Index

Sommario/riassunto

This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field. ContentsPart I: BasicsModel examplesCategories and functorsC∗-algebrasPart II: Noncommutative invariantsTopologyAlgebraic geometryNumber theoryPart III: Brief survey of NCGFinite geometriesContinuous geometriesConnes geometriesIndex theoryJones polynomialsQuantum groupsNoncommutative algebraic geometryTrends in noncommutative geometry