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＜電子ブック＞
Introduction to ℓ²-invariants / by Holger Kammeyer
(Lecture Notes in Mathematics. ISSN:16179692 ; 2247)

版	1st ed. 2019.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2019
大きさ	VIII, 183 p. 37 illus : online resource
著者標目	*Kammeyer, Holger author SpringerLink (Online service)
件　名	LCSH:Algebraic topology LCSH:Manifolds (Mathematics) LCSH:Functional analysis LCSH:Group theory FREE:Algebraic Topology FREE:Manifolds and Cell Complexes FREE:Functional Analysis FREE:Group Theory and Generalizations
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-030-28297-4

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