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Knygos aprašymas

This book introduces the reader to the most important concepts and problems in the field of ¿²-invariants. After some foundational material on group von Neumann algebras, ¿²-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of ¿²-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of ¿²-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 ¿²-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.

Informacija

Autorius: Holger Kammeyer
Serija: Lecture Notes in Mathematics
Leidėjas: Springer International Publishing
Išleidimo metai: 2019
Knygos puslapių skaičius: 192
ISBN-10: 3030282961
ISBN-13: 9783030282967
Formatas: Knyga minkštu viršeliu
Kalba: Anglų
Žanras: Functional analysis and transforms

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