New York Journal of Mathematics
Volume 22 (2016) 115-190


Colin D. Reid

Dynamics of flat actions on totally disconnected, locally compact groups

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Published: February 11, 2016
Keywords: T.d.l.c. groups, tidy theory
Subject: 22D05

Let G be a totally disconnected, locally compact group and let H be a virtually flat (for example, polycyclic) group of automorphisms of G. We study the structure of, and relationships between, various subgroups of G defined by the dynamics of H. In particular, we consider the following four subgroups: the intersection of all tidy subgroups for H on G (in the case that H is flat); the intersection of all H-invariant open subgroups of G; the smallest closed H-invariant subgroup D such that no H-orbit on G/D accumulates at the trivial coset; and the group generated by the closures of contraction groups of elements of H on G.


The author is an ARC DECRA fellow. Research supported in part by ARC Discovery Project DP120100996.

Author information

University of Newcastle, School of Mathematical and Physical Sciences, Callaghan, NSW 2308, Australia