Introduction to ℓ²-invariants

Holger Kammeyer (Autor)

Buch | Softcover

VIII, 183 Seiten

2019 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-28296-7 (ISBN)

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This book introduces the reader to the most important concepts and problems in the field of ²-invariants. After some foundational material on group von Neumann algebras, ²-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of ²-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of ²-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 ²-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.

Holger Kammeyer studied Mathematics at Goettingen 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 (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.

"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)

Erscheinungsdatum	01.11.2019
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	VIII, 183 p. 37 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	302 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	²-Betti Numbers • ²-invariants • ²-torsion • ℓ ²-Betti Numbers • ℓ ²-invariants • ℓ ²-torsion • Lück Approximation • Torsion Growth
ISBN-10	3-030-28296-1 / 3030282961
ISBN-13	978-3-030-28296-7 / 9783030282967
Zustand	Neuware