Introduction to l2-invariants

• 作者： Kammeyer, Holger, author.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Lecture notes in mathematics ;
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Lecture notes in mathematics,2247
• 主題： Invariants. , Algebraic Topology. , Manifolds and Cell Complexes (incl. Diff.Topology) , Functional Analysis. , Group Theory and Generalizations.
• ISBN： 9783030282974 (electronic bk.) 、 9783030282967 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
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• 摘要註: 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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