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Introduction to ℓ²-invariants / by Holger Kammeyer
(Lecture Notes in Mathematics. ISSN:16179692 ; 2247)
版 | 1st ed. 2019. |
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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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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783030282974 |
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EB00210772 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA612-612.8 DC23:514.2 |
書誌ID | 4000134966 |
ISBN | 9783030282974 |
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