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-${Z}^{d}$ 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