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Dynamics of non-archimedean Polish groups

Kechris, Alexander S. (2012) Dynamics of non-archimedean Polish groups. In: European Congress of Mathematics, Kraków, 2-7 July, 2012. European Mathematical Society , Zurich, Switzerland, pp. 375-397. ISBN 978-3-03719-120-0.

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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.

Item Type:Book Section
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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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Subject Keywords:Non-archimedean groups, Fraïssé theory, Ramsey theory, ample genericity, automatic continuity, unique ergodicity, spatial realizations, unitary representations
Classification Code:2010 Mathematics Subject Classification. Primary 03C15, 22F50, 54H20, 37A15.
Record Number:CaltechAUTHORS:20180803-160520242
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88576
Deposited By: George Porter
Deposited On:03 Aug 2018 23:26
Last Modified:16 Nov 2021 00:28

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