[Download] "Introduction to ℓ²-invariants" by Holger Kammeyer * eBook PDF Kindle ePub Free

April 27, 2021

eBook details

Title: Introduction to ℓ²-invariants
Author : Holger Kammeyer
Release Date : January 29, 2019
Genre: Mathematics,Books,Science & Nature,
Pages : * pages
Size : 6132 KB

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.

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