Connected Polish groups with ample generics

Abstract

In this paper, we give the first examples of connected Polish groups that have ample generics, answering a question of Kechris and Rosendal. We show that any Polish group with ample generics embeds into a connected Polish group with ample generics and that full groups of type III hyperfinite ergodic equivalence relations have ample generics. We also sketch a proof of the following result: the full group of any type III ergodic equivalence relation has topological rank 2.

New version mentioning the results Malicki obtained independently and simultaneously http://arxiv.org/abs/1503.03919, which also answer Kechris and Rosendal's question in a different way. Comments welcome!

References in corpus (1)

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

Cited by in corpus (2)

• Concentration of measure, classification of submeasures, and dynamics of $L_0$
• Isometry group of Borel randomizations