Dynamics of non-archimedean Polish groups

  • Alexander S. Kechris

    California Institute of Technology, Pasadena, USA
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A topological group 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 pro finite groups and () 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, fi nite 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.