The flat closing problem for buildings

Ciobotaru, Corina

doi:10.2140/agt.2014.14.3089

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The flat closing problem for buildings

Corina Ciobotaru

Algebraic & Geometric Topology 14 (2014) 3089–3096

DOI: 10.2140/agt.2014.14.3089

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- $Z^{d}$ 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

Volume 14, issue 5 (2014)