Introduction to l[2]-invariants
著者
書誌事項
Introduction to l[2]-invariants
（Lecture notes in mathematics, 2247）
Springer, c2019
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注記
Includes bibliographical references (p. 165-172) and index
[2] is superscript
内容説明・目次
内容説明
This book introduces the reader to the most important concepts and problems in the field of (2)-invariants. After some foundational material on group von Neumann algebras, (2)-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of (2)-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of (2)-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 (2)-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.
目次
- Introduction. - Hilbert Modules and von Neumann Dimension. - l2-Betti Numbers of CW Complexes. - l2-Betti Numbers of Groups. - Luck's Approximation Theorem. - Torsion Invariants.
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