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Published July 2012 | Accepted Version
Book Section - Chapter Open

Dynamics of non-archimedean Polish groups

Abstract

A topological group G is Polish if its topology admits a compatible separable complete metric. Such a group is non-archimedean if it has a basis at the identity that consists of open subgroups. This class of Polish groups includes the profinite groups and (ℚ_p, +) but our main interest here will be on non-locally compact groups. In recent years there has been considerable activity in the study of the dynamics of Polish non-archimedean groups and this has led to interesting interactions between logic, finite combinatorics, group theory, topological dynamics, ergodic theory and representation theory. In this paper I will give a survey of some of the main directions in this area of research.

Additional Information

© 2014 EMS Publishing House. Work on this paper was partially supported by NSF Grant DMS-0968710. I would like to thank J. Melleray, L. Nguyen Van Thé, C. Rosendal, M. Sokić, S. Solecki, S. Thomas and T. Tsankov for many helpful comments on an earlier draft of this paper

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