02149nmm a2200349 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002100139245008200160250001700242260005600259300004300315653002200358653002300380653002400403653001700427653003700444653002400481653002300505653002800528653005500556710003400611041001900645989003600664490003300700856007200733082001000805520098400815EB001875587EBX0100000000000000103895400000000000000.0cr|||||||||||||||||||||191108 ||| eng a97830302829741 aKammeyer, Holger00aIntroduction to ℓ²-invariantshElektronische Ressourcecby Holger Kammeyer a1st ed. 2019 aChambSpringer International Publishingc2019, 2019 aVIII, 183 p. 37 illusbonline resource aComplex manifolds aAlgebraic Topology aFunctional analysis aGroup theory aGroup Theory and Generalizations aFunctional Analysis aAlgebraic topology aManifolds (Mathematics) aManifolds and Cell Complexes (incl. Diff.Topology)2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aLecture Notes in Mathematics uhttps://doi.org/10.1007/978-3-030-28297-4?nosfx=yxVerlag3Volltext0 a514.2 aThis 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