Volume 14, issue 5 (2014)

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The flat closing problem for buildings

Corina Ciobotaru

Algebraic & Geometric Topology 14 (2014) 3089–3096
Abstract

Using the notion of a strongly regular hyperbolic automorphism of a locally finite Euclidean building, we prove that any (not necessarily discrete) closed, cocompact subgroup of the type-preserving automorphisms group of a locally finite general nonspherical building contains a compact-by-Zd subgroup, where d is the dimension of a maximal flat.

Keywords
groups acting on buildings, Gromov's flat closing problem
Mathematical Subject Classification 2000
Primary: 57S25, 51E24
Secondary: 20E42, 20F55
References
Publication
Received: 5 November 2013
Revised: 20 March 2014
Accepted: 20 March 2014
Published: 5 November 2014
Authors
Corina Ciobotaru
Institut de recherche en mathématique et physique (IRMP)
UCL
Chemin du Cyclotron 2
bte L7.01.01
1348 Louvain-la-Neuve
Belgium