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

Groves, Daniel (2005) Limits of (certain) CAT(0) groups, I: Compactification. Algebraic and Geometric Topology, 5 (52). pp. 1325-1364. ISSN 1472-2747. doi:10.2140/agt.2005.5.1325.

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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 [18]. 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.

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Additional Information:Submitted: 14 January 2005. Accepted: 20 September 2005. Published: 6 October 2005.
Subject Keywords:CAT(0) spaces, isolated flats, Limit groups, R-trees
Issue or Number:52
Record Number:CaltechAUTHORS:GROagt05
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1176
Deposited By: Archive Administrator
Deposited On:02 Jan 2006
Last Modified:08 Nov 2021 19:08

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