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

Groves, Daniel

doi:10.2140/agt.2005.5.1325

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

Daniel Groves

Algebraic & Geometric Topology 5 (2005) 1325–1364

DOI: 10.2140/agt.2005.5.1325

arXiv: math.GR/0404440

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, $\mathbb{R}$–trees

Mathematical Subject Classification 2000

Primary: 20F65

Secondary: 20F67, 20E08, 57M07

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Publication

Received: 14 January 2005

Accepted: 20 September 2005

Published: 6 October 2005

Authors

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

Volume 5, issue 4 (2005)