Introduction to ℓ²-invariants
Kammeyer, Holger.
Introduction to ℓ²-invariants [electronic resource] / by Holger Kammeyer. - 1st ed. 2019. - VIII, 183 p. 37 illus. online resource. - Lecture Notes in Mathematics, 2247 0075-8434 ; . - Lecture Notes in Mathematics, 2247 .
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.
9783030282974
10.1007/978-3-030-28297-4 doi
Indica Technologies & Services Pvt. Ltd., 7/31, Ansari Road, Daryaganj, New Delhi-110002
Algebraic topology.
Manifolds (Mathematics).
Complex manifolds.
Functional analysis.
Group theory.
Algebraic Topology.
Manifolds and Cell Complexes (incl. Diff.Topology).
Functional Analysis.
Group Theory and Generalizations.
QA612-612.8
514.2
Introduction to ℓ²-invariants [electronic resource] / by Holger Kammeyer. - 1st ed. 2019. - VIII, 183 p. 37 illus. online resource. - Lecture Notes in Mathematics, 2247 0075-8434 ; . - Lecture Notes in Mathematics, 2247 .
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.
9783030282974
10.1007/978-3-030-28297-4 doi
Indica Technologies & Services Pvt. Ltd., 7/31, Ansari Road, Daryaganj, New Delhi-110002
Algebraic topology.
Manifolds (Mathematics).
Complex manifolds.
Functional analysis.
Group theory.
Algebraic Topology.
Manifolds and Cell Complexes (incl. Diff.Topology).
Functional Analysis.
Group Theory and Generalizations.
QA612-612.8
514.2