UID:
edoccha_9959338365202883
Umfang:
1 online resource (190 pages) :
,
illustrations.
Ausgabe:
1st ed. 2019.
ISBN:
3-030-28297-X
Serie:
Lecture Notes in Mathematics, 2247
Inhalt:
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.
Weitere Ausg.:
ISBN 3-030-28296-1
Sprache:
Englisch
DOI:
10.1007/978-3-030-28297-4
