A Measurable-Group-Theoretic Solution to von Neumann's Problem
Damien Gaboriau (UMPA-ENSL), Russell Lyons
TL;DR
This paper provides a measurable-group-theoretic solution to von Neumann's problem, demonstrating that non-amenable groups contain free subgroups and embedding free-group factors into wreath product factors.
Contribution
It offers a new measurable-group-theoretic approach to von Neumann's problem and establishes embedding results for free-group von Neumann factors.
Findings
Non-amenable groups contain non-cyclic free subgroups.
Embedding of free-group von Neumann factors into wreath product factors.
Positive measurable-group-theoretic resolution of von Neumann's problem.
Abstract
We give a positive answer, in the measurable-group-theory context, to von Neumann's problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get an embedding result of the free-group von Neumann factor into restricted wreath product factors.
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