Introduction to ℓ²-invariants: 2247 (Lecture Notes in Mathematics) - Softcover

Kammeyer, Holger

 
9783030282967: Introduction to ℓ²-invariants: 2247 (Lecture Notes in Mathematics)
Softcover
ISBN 10: 3030282961 ISBN 13: 9783030282967
Verlag: Springer, 2019

Inhaltsangabe

This book introduces the reader to the most important concepts and problems in the field of ℓ²-invariants. After some foundational material on group von Neumann algebras, ℓ²-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of ℓ²-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of ℓ²-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 ℓ²-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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Über die Autorin bzw. 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 ℓ ²-invariants forms a recurrent theme in his work. He has given introductory courses on the matter on various occasions.

Von der hinteren Coverseite

This book introduces the reader to the most important concepts and problems in the field of l²-invariants. After some foundational material on group von Neumann algebras, l²-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of l²-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of l²-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 l²-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 diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2019
Sprache
Englisch
ISBN 10 
3030282961
ISBN 13 
9783030282967
Einband
Tapa blanda
Auflage
1
Anzahl der Seiten
192
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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