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Introduction to (2)-invariants
Lecture Notes in Mathematics 2247
Synopsis
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 Luck'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.
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What Reviewers Are Saying
"This is an excellent introductory book, to be recommended to readers looking for an introduction to the field, as well as those that want to have an overview of recent developments." (Joan Porti, Mathematical Reviews, September, 2020)