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Cover: 9783030282967 | Introduction to ¿²-invariants | Holger Kammeyer | Taschenbuch | VIII
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Introduction to ¿²-invariants
Taschenbuch von Holger Kammeyer
Sprache: Englisch

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Beschreibung
This book introduces the reader to the most important concepts and problems in the field of ¿²-invariants. After some foundational material on group von Neumann algebras, ¿²-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of ¿²-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of ¿²-Betti numbers allows for applications in group theory. A whole chapter is dedicated to Lück's approximation theorem and its generalizations. The final chapter deals with ¿²-torsion, twisted variants and the conjectures relating them to torsion growth in homology.
The text provides a self-contained treatment that constructs the required specialized concepts from scratch. It comes with numerous exercises and examples, so that both graduate students and researchers will find it useful for self-study or as a basis for an advanced lecture course.
This book introduces the reader to the most important concepts and problems in the field of ¿²-invariants. After some foundational material on group von Neumann algebras, ¿²-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of ¿²-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of ¿²-Betti numbers allows for applications in group theory. A whole chapter is dedicated to Lück's approximation theorem and its generalizations. The final chapter deals with ¿²-torsion, twisted variants and the conjectures relating them to torsion growth in homology.
The text provides a self-contained treatment that constructs the required specialized concepts from scratch. It comes with numerous exercises and examples, so that both graduate students and researchers will find it useful for self-study or as a basis for an advanced lecture course.
Über den Autor

Holger Kammeyer studied Mathematics at Göttingen and Berkeley. After a postdoc position in Bonn he is now based at Karlsruhe Institute of Technology. His research interests range around algebraic topology and group theory. The application of ¿ ²-invariants forms a recurrent theme in his work. He has given introductory courses on the matter on various occasions.

Zusammenfassung

An up-to-date and user-friendly introduction to the rapidly developing field of l²-invariants

Proceeds quickly to the research level after thoroughly covering all the basics

Contains many motivating examples, illustrations, and exercises

Inhaltsverzeichnis
- Introduction. - Hilbert Modules and von Neumann Dimension. - l2-Betti Numbers of CW Complexes. - l2-Betti Numbers of Groups. - Lück's Approximation Theorem. - Torsion Invariants.
Details
Erscheinungsjahr: 2019
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 192
Reihe: Lecture Notes in Mathematics
Inhalt: viii
183 S.
37 s/w Illustr.
183 p. 37 illus.
ISBN-13: 9783030282967
ISBN-10: 3030282961
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Kammeyer, Holger
Auflage: 1st ed. 2019
Hersteller: Springer International Publishing
Springer International Publishing AG
Lecture Notes in Mathematics
Maße: 235 x 155 x 11 mm
Von/Mit: Holger Kammeyer
Erscheinungsdatum: 31.10.2019
Gewicht: 0,3 kg
preigu-id: 116920867
Über den Autor

Holger Kammeyer studied Mathematics at Göttingen and Berkeley. After a postdoc position in Bonn he is now based at Karlsruhe Institute of Technology. His research interests range around algebraic topology and group theory. The application of ¿ ²-invariants forms a recurrent theme in his work. He has given introductory courses on the matter on various occasions.

Zusammenfassung

An up-to-date and user-friendly introduction to the rapidly developing field of l²-invariants

Proceeds quickly to the research level after thoroughly covering all the basics

Contains many motivating examples, illustrations, and exercises

Inhaltsverzeichnis
- Introduction. - Hilbert Modules and von Neumann Dimension. - l2-Betti Numbers of CW Complexes. - l2-Betti Numbers of Groups. - Lück's Approximation Theorem. - Torsion Invariants.
Details
Erscheinungsjahr: 2019
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 192
Reihe: Lecture Notes in Mathematics
Inhalt: viii
183 S.
37 s/w Illustr.
183 p. 37 illus.
ISBN-13: 9783030282967
ISBN-10: 3030282961
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Kammeyer, Holger
Auflage: 1st ed. 2019
Hersteller: Springer International Publishing
Springer International Publishing AG
Lecture Notes in Mathematics
Maße: 235 x 155 x 11 mm
Von/Mit: Holger Kammeyer
Erscheinungsdatum: 31.10.2019
Gewicht: 0,3 kg
preigu-id: 116920867
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