A survey of Measured Group Theory
Alex Furman

TL;DR
This survey reviews recent advances in measured group theory, focusing on measure and orbit equivalence, invariants, and rigidity phenomena in the classification of infinite groups and their actions.
Contribution
It provides a comprehensive overview of measure and orbit equivalence, highlighting key invariants and rigidity results in the classification of groups and their actions.
Findings
Summary of measure equivalence invariants
Overview of orbit equivalence classification results
Discussion of rigidity phenomena in measured group theory
Abstract
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 ergodic 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.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Geometric and Algebraic Topology · Advanced Algebra and Geometry
