A SURVEY OF MEASURED GROUP THEORY

By A. Furman. 2009

105 citations recorded by the source corpus.

The title refers to the area of research which studies infinite groups using measure-theoretic tools, and studies the restrictions that group structure imposes on er- godic theory of their actions. The paper is a survey of recent developments focused on the notion of Measure Equivalence between groups, and Orbit Equivalence between group actions. We discuss known invariants and classification results (rigidity) in both areas.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/25a68b3b9a3bcd56b49a53f12742f6265eb8277f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. I. Chifan
2. Adrian Ioana
3. Xin Li
4. J. Renault
5. S. Vaes
6. Sorin Popa
7. J. Peterson
8. Thomas Sinclair

In Mathematical Physics

1. Xin Li
2. I. Chifan
3. Adrian Ioana
4. J. Renault
5. S. Vaes
6. Sorin Popa
7. Aidan Sims
8. Mihaita Berbec

Citations in the corpus

• Cartan subalgebras in C*-algebras. Existence and uniqueness (2017, result): “The situation we are describing here is completely analogous to the measurable framework, where a fruitful interplay between Cartan subalgebras in von Neumann algebras (vN-algebras), orbit equivalence for measure-preserving dynamical systems and geometric group theory has been established [56, 20, 1”
• Integrable measure equivalence and rigidity of hyperbolic lattices (2010, unknown): “Tautening maps 37 A.4.”
• Acylindrical hyperbolicity of groups acting on trees (2013, unknown): “On the other hand, it is well known that being amenable is also a measure equivalence invariant (see, for example, [36]).”
• Ergodic Subequivalence Relations Induced by a Bernoulli Action (2008, background): “During the past decade, the study of countable measure preserving equivalence relations has received a lot of attention with many new rigidity phenomena having been discovered (see the surveys [Sh], [Po5], [ Fu ]).”