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

• 成果类型: Article
• 署名作者: Le Maitre, Francois
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0503-6
• 发表日期: 2014
• 页码: 261-268
• 关键词: cost

摘要

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.