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Introduction to ℓ²-invariants

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Introduction to ℓ²-invariants/ by Holger Kammeyer.
Author:	Kammeyer, Holger.
Description:	VIII, 183 p. 37 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Algebraic topology. -
Online resource:	https://doi.org/10.1007/978-3-030-28297-4
ISBN:	9783030282974

Introduction to ℓ²-invariants
Kammeyer, Holger.

Introduction to ℓ²-invariants[electronic resource] /by Holger Kammeyer. - 1st ed. 2019. - VIII, 183 p. 37 illus.online resource. - Lecture Notes in Mathematics,22470075-8434 ;. - Lecture Notes in Mathematics,2144.

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.

ISBN: 9783030282974

Standard No.: 10.1007/978-3-030-28297-4doiSubjects--Topical Terms:

678206
Algebraic topology.

LC Class. No.: QA612-612.8

Dewey Class. No.: 514.2

Introduction to ℓ²-invariants
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