Introduction to l2-invariants e-bog

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