TY  - BOOK
AU  - Kammeyer,Holger
ED  - SpringerLink (Online service)
TI  - Introduction to ℓ²-invariants
T2  - Lecture Notes in Mathematics,
SN  - 9783030282974
AV  - QA612-612.8 
U1  - 514.2 23
PY  - 2019///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Algebraic topology
KW  - Manifolds (Mathematics)
KW  - Complex manifolds
KW  - Functional analysis
KW  - Group theory
KW  - Algebraic Topology
KW  - Manifolds and Cell Complexes (incl. Diff.Topology)
KW  - Functional Analysis
KW  - Group Theory and Generalizations
N2  - 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
UR  - https://doi.org/10.1007/978-3-030-28297-4
ER  -