Algebraic and Geometric Topology 5 (2005), paper no. 52, pages 1325-1364.

Limits of (certain) CAT(0) groups, I: Compactification

Daniel Groves

Abstract. The purpose of this paper is to investigate torsion-free groups which act properly and cocompactly on CAT(0) metric spaces which have isolated flats, as defined by Hruska. Our approach is to seek results analogous to those of Sela, Kharlampovich and Miasnikov for free groups and to those of Sela (and Rips and Sela) for torsion-free hyperbolic groups. This paper is the first in a series. In this paper we extract an R-tree from an asymptotic cone of certain CAT(0) spaces. This is analogous to a construction of Paulin, and allows a great deal of algebraic information to be inferred, most of which is left to future work.

Keywords. CAT(0) spaces, isolated flats, Limit groups, R-trees

AMS subject classification. Primary: 20F65. Secondary: 20F67, 20E08, 57M07.

E-print: arXiv:math.GR/0404440

DOI: 10.2140/agt.2005.5.1325

Submitted: 14 January 2005. Accepted: 20 September 2005. Published: 6 October 2005.

Notes on file formats

Daniel Groves
Department of Mathematics, California Institute of Technology
Pasadena, CA, 91125, USA

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