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Introduction to l²-invariants

Af: Holger Kammeyer Engelsk Paperback

Introduction to l²-invariants

Af: Holger Kammeyer Engelsk Paperback
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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.
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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.
Produktdetaljer
Sprog: Engelsk
Sider: 183
ISBN-13: 9783030282967
Indbinding: Paperback
Udgave:
ISBN-10: 3030282961
Udg. Dato: 31 okt 2019
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 31 okt 2019
Forfatter(e): Holger Kammeyer
Forfatter(e) Holger Kammeyer


Kategori Funktionsanalyse og transformation


ISBN-13 9783030282967


Sprog Engelsk


Indbinding Paperback


Sider 183


Udgave


Længde 0mm


Bredde 155mm


Højde 235mm


Udg. Dato 31 okt 2019


Oplagsdato 31 okt 2019


Forlag Springer Nature Switzerland AG

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