Introduction to ℓ²-invariants

von Holger Kammeyer

183 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Mathematics
• ISBN: 9783030282967
• Sprache: Englisch
• Erscheinungsdatum: 31.10.2019
• Genre: Mathematik/Geometrie
• Verlag: Springer International Publishing