Introduction to ¿²-invariants

1. Auflage 2019
ISBN: 978-3-030-28296-7
Verlag: Springer International Publishing

Buch, Englisch, Band 2247, 183 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 300 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Kammeyer, Holger

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

- Introduction. - Hilbert Modules and von Neumann Dimension. - l2-Betti Numbers of CW Complexes. - l2-Betti Numbers of Groups. - Lück’s Approximation Theorem. - Torsion Invariants.

Über Autor(innen)

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.