Introduction to l2-invariants

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  • Introduction to l2-invariants Book Detail

  • Author : Holger Kammeyer
  • Release Date : 2019-10-29
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 190
  • ISBN 13 : 303028297X
  • File Size : 15,15 MB

Introduction to l2-invariants by Holger Kammeyer PDF Summary

Book 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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