Introduction to ¿²-invariants | Taschenbuch

Cover: 9783030282967 | Introduction to ¿²-invariants | Holger Kammeyer | Taschenbuch | viii

Rückseite: 9783030282967 | Introduction to ¿²-invariants | Holger Kammeyer | Taschenbuch | viii

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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.

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 , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
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
Einband:	Kartoniert / Broschiert
Autor:	Kammeyer, Holger
Hersteller:	Springer Springer VS Springer International Publishing AG Lecture Notes in Mathematics
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 11 mm
Von/Mit:	Holger Kammeyer
Erscheinungsdatum:	31.10.2019
Gewicht:	0,3 kg