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.
Rezensionen / Stimmen
"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)
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Zielgruppe
Illustrationen
37
37 s/w Abbildungen
VIII, 183 p. 37 illus.
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 11 mm
Gewicht
ISBN-13
978-3-030-28296-7 (9783030282967)
DOI
10.1007/978-3-030-28297-4
Schweitzer Klassifikation
Holger Kammeyer studied Mathematics at Göttingen and Berkeley. After a postdoc position in Bonn he is now based at Karlsruhe Institute of Technology. His research interests range around algebraic topology and group theory. The application of l ²-invariants forms a recurrent theme in his work. He has given introductory courses on the matter on various occasions.
- Introduction. - Hilbert Modules and von Neumann Dimension. - l2-Betti Numbers of CW Complexes. - l2-Betti Numbers of Groups. - Lück's Approximation Theorem. - Torsion Invariants.
