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|a 9783030282974
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|a 10.1007/978-3-030-28297-4
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|a Kammeyer, Holger.
|e author.
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|4 http://id.loc.gov/vocabulary/relators/aut
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|a Introduction to ℓ²-invariants
|h [electronic resource] /
|c by Holger Kammeyer.
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|a 1st ed. 2019.
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|a Cham :
|b Springer International Publishing :
|b Imprint: Springer,
|c 2019.
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|a VIII, 183 p. 37 illus.
|b online resource.
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|a text
|b txt
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|a computer
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|a text file
|b PDF
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 2247
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|a 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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|a Algebraic topology.
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|a Manifolds (Mathematics).
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|a Complex manifolds.
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|a Functional analysis.
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|a Group theory.
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|a Algebraic Topology.
|0 http://scigraph.springernature.com/things/product-market-codes/M28019
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|a Manifolds and Cell Complexes (incl. Diff.Topology).
|0 http://scigraph.springernature.com/things/product-market-codes/M28027
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|a Functional Analysis.
|0 http://scigraph.springernature.com/things/product-market-codes/M12066
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|a Group Theory and Generalizations.
|0 http://scigraph.springernature.com/things/product-market-codes/M11078
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783030282967
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|i Printed edition:
|z 9783030282981
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 2247
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|u https://doi.org/10.1007/978-3-030-28297-4
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a Mathematics and Statistics (Springer-11649)
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