Dynamics of flat actions on totally disconnected, locally compact groups

Abstract

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 $G$.

81 pages; accepted version. Final published version is here: http://nyjm.albany.edu/j/2016/22-6.html

References in corpus (2)

• Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups
• Tidy subgroups for commuting automorphisms of totally disconnected groups: an analogue of simultaneous triangularisation of matrices

Cited by in corpus (1)

• Indicability, residual finiteness, and simple subquotients of groups acting on trees