Titlebook: Introduction to ?2-invariants; Holger Kammeyer Book 2019 The Editor(s) (if applicable) and The Author(s), under exclusive license to Sprin

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懶惰人民

,-Betti Numbers of Groups,n Neumann dimension to arbitrary modules over the group von Neumann algebra. This leads to the definition of ..-Betti numbers of arbitrary .-spaces and hence allows the definition of ..-Betti numbers of general discrete countable groups via classifying spaces. We give example computations for variou

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,Lück’s Approximation Theorem,Banach-, ..-, and von Neumann algebras. The proof is then presented in a manner that emphasizes the two main ingredients: weak convergence of spectral measures and the logarithmic bound on spectral distribution functions. We discuss in detail in how far some of the assumptions in the theorem can be

純樸

MONY

,-Betti Numbers of CW Complexes,iscuss Atiyah’s question on possible values of ..-Betti numbers and expound how this is relevant for Kaplansky’s zero divisor conjecture. The chapter concludes with proofs that positive ..-Betti numbers obstruct self-coverings, mapping torus structures, and circle actions on even dimensional hyperbolic manifolds.

不在灌木叢中

Chromatic

Morphine

Torsion Invariants,ic setting, we present the Bergeron Venkatesh conjecture on torsion in twisted homology. We conclude the text with an account on profinite rigidity, (non-)profiniteness of ..-Betti numbers and a proof that the torsion approximation conjecture implies profiniteness of volume for 3-manifolds.

Euphonious

Gerontology

0075-8434 horoughly covering all the basics.Contains many motivating eThis book introduces the reader to the most important concepts and problems in the field of ?2-invariants. After some foundational material on group von Neumann algebras, ?2-Betti numbers are defined and their use is illustrated by several