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The Dynamical View: Measured Group Theory

  • Clara LöhEmail author
Chapter
  • 36 Downloads
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

The theory of von Neumann algebras can be viewed as a model of non-commutative measure theory. Therefore, it is plausible that L2-Betti numbers can be computed in terms of probability measure preserving actions.
  • On the one hand, this leads to an additional way of computing L2-Betti numbers of groups.

  • On the other hand, in this way, L2-Betti numbers provide orbit equivalence invariants.

We will first recall basic terminology from measured group theory. Then we will study L2-Betti numbers of standard equivalence relations. Moreover, we will discuss cost and its relation with the first L2-Betti number and rank gradients.

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Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany

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