Geometry & Topology 9 (2005) 1501–1538

DOI: 10.2140/gt.2005.9.1501

Erratum: Geometry & Topology 13 (2009) 699–707

Abstract

We explore the geometry of nonpositively curved spaces with isolated flats, and its consequences for groups that act properly discontinuously, cocompactly, and isometrically on such spaces. We prove that the geometric boundary of the space is an invariant of the group up to equivariant homeomorphism. We also prove that any such group is relatively hyperbolic, biautomatic, and satisfies the Tits Alternative. The main step in establishing these results is a characterization of spaces with isolated flats as relatively hyperbolic with respect to flats. Finally we show that a CAT(0) space has isolated flats if and only if its Tits boundary is a disjoint union of isolated points and standard Euclidean spheres. In an appendix written jointly with Hindawi, we extend many of the results of this article to a more general setting in which the isolated subspaces are not required to be flats.

Keywords

isolated flats, asymptotic cone, relative hyperbolicity

Mathematical Subject Classification

Primary: 20F67

Secondary: 20F69

References

Publication

Received: 5 April 2005
Revised: 25 July 2005
Accepted: 24 June 2005
Published: 8 August 2005
Proposed: Walter Neumann
Seconded: Martin Bridson, Benson Farb

Authors