The number of topological generators for full groups of ergodic equivalence relations

Abstract

We completely elucidate the relationship between two invariants associated with an ergodic probability measure-preserving (pmp) equivalence relation, namely its cost and the minimal number of topological generators of its full group. It follows that for any free pmp ergodic action of the free group on $n$ generators, the minimal number of topological generators for the full group of the action is $n+1$, answering a question of Kechris.

The numbering of the results is now the same as in the published version

Cited by in corpus (6)

• Connected Polish groups with ample generics
• On dense totipotent free subgroups in full groups
• Generic IRS in free groups, after Bowen
• Highly faithful actions and dense free subgroups in full groups
• Topological generators for full groups of hyperfinite pmp equivalence relations
• Infinitesimal generators and quasi non-archimedean topological groups