Geometric characterization of flat groups of automorphisms

Title: Geometric characterization of flat groups of automorphisms
Creator: Baumgartner, Udo; Schlichting, Günter; Willis, George
Relation: Groups, Geometry, and Dynamics Vol. 4, Issue 1, p. 1-13
Relation: http://www.ems-ph.org/journals/show_issue.php?issn=1661-7207&vol=4&iss=1
Publisher: European Mathematical Society Publishing House
Resource Type: journal article
Date: 2010
Description: If ℋ is a flat group of automorphisms of finite rank n of a totally disconnected, locally compact group G, then each orbit of ℋ in the metric space ℬ(G) of compact, open subgroups of G is quasi-isometric to n-dimensional Euclidean space. In this note we prove the following partial converse: Assume that G is a totally disconnected, locally compact group such that ℬ (G) is a proper metric space and let ℋ be a group of automorphisms of G such that some (equivalently every) orbit of ℋ in ℬ(G) is quasi-isometric ton-dimensional Euclidean space, then ℋ has a finite index subgroup which is flat of rank n. We can draw this conclusion under weaker assumptions. We also single out a naturally defined flat subgroup of such groups of automorphisms.
Subject: totally disconnected locally compact group; automorphism group; tidy subgroup; rank; quasi-isometry; flat
Identifier: http://hdl.handle.net/1959.13/931210
Identifier: uon:11018
Identifier: ISSN:1661-7207
Language: eng
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