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
Email: groves@caltech.edu
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