UID:
almahu_9949198438302882
Format:
VIII, 183 p. 37 illus.
,
online resource.
Edition:
1st ed. 2019.
ISBN:
9783030282974
Series Statement:
Lecture Notes in Mathematics, 2247
Content:
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.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783030282967
Additional Edition:
Printed edition: ISBN 9783030282981
Language:
English
DOI:
10.1007/978-3-030-28297-4
URL:
https://doi.org/10.1007/978-3-030-28297-4
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