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Introduction to l2-invariants

Kammeyer, Holger.

Introduction to l2-invariants

Record Type:	Electronic resources : Monograph/item
Title/Author:	Introduction to l2-invariantsby Holger Kammeyer.
Author:	Kammeyer, Holger.
Published:	Cham :Springer International Publishing :2019.
Description:	viii, 183 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Invariants.
Online resource:	https://doi.org/10.1007/978-3-030-28297-4
ISBN:	9783030282974$q(electronic bk.)

Introduction to l2-invariants
Kammeyer, Holger.

Introduction to l2-invariants[electronic resource] /by Holger Kammeyer. - Cham :Springer International Publishing :2019. - viii, 183 p. :ill., digital ;24 cm. - Lecture notes in mathematics,22470075-8434 ;. - Lecture notes in mathematics ;2035..

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 Luck'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.graduate students and researchers will find it useful for self-studying or as basis for an advanced lecture course.

ISBN: 9783030282974$q(electronic bk.)

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

230047
Invariants.

LC Class. No.: QA201 / .K366 2019

Dewey Class. No.: 514.2

Introduction to l2-invariants
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520 $a 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 Luck'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.graduate students and researchers will find it useful for self-studying or as basis for an advanced lecture course.
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