Introduction to l²-invariants
Published on 29. October 2019
VIII, 183 pages
978-3-030-28297-4 (ISBN)
Description
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.
Reviews / Votes
"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)
More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
VIII, 183 p. 37 illus.
File size
3,62 MB
ISBN-13
978-3-030-28297-4 (9783030282974)
DOI
10.1007/978-3-030-28297-4
Schweitzer Classification
Other editions
Additional editions
Holger Kammeyer
Introduction to l²-invariants
Book
10/2019
1st Edition
Springer
€53.49
Shipment within 7-9 days
Person
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.
Content
- Introduction. - Hilbert Modules and von Neumann Dimension. - l2-Betti Numbers of CW Complexes. - l2-Betti Numbers of Groups. - Lück's Approximation Theorem. - Torsion Invariants.
