Connected Polish groups with ample generics
Group Theory
2017-05-17 v2 Dynamical Systems
Logic
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.
Keywords
Cite
@article{arxiv.1503.04298,
title = {Connected Polish groups with ample generics},
author = {Adriane Kaïchouh and François Le Maître},
journal= {arXiv preprint arXiv:1503.04298},
year = {2017}
}
Comments
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!