# 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.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00787328
Contributor : François Le Maître <>
Submitted on : Monday, February 11, 2013 - 6:48:15 PM
Last modification on : Tuesday, November 19, 2019 - 10:19:53 AM
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### Citation

François Le Maître. The number of topological generators for full groups of ergodic equivalence relations. Inventiones Mathematicae, Springer Verlag, 2014, pp.261-268. ⟨10.1007/s00222-014-0503-6⟩. ⟨ensl-00787328⟩

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