Introduction to ℓ²-invariants eBook
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Author(s): Holger Kammeyer
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Publisher: Springer
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Print ISBN: 9783030282967, 3030282961
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eText ISBN: 9783030282974, 303028297X
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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.
This is a digital product.
Introduction to ℓ²-invariants is written by Holger Kammeyer and published by Springer. The Digital and eTextbook ISBNs for Introduction to ℓ²-invariants are 9783030282974, 303028297X and the print ISBNs are 9783030282967, 3030282961.
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