EAN: 9783030282967

INTRODUCTION TO ²-INVARIANTS - HOLGER KAMMEYER ...

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.

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