Geometry & Topology, Vol. 8 (2004)
Paper no. 5, pages 205--275.
Nonpositively curved 2-complexes with isolated flats
G Christopher Hruska
Abstract.
We introduce the class of nonpositively curved 2-complexes with the
Isolated Flats Property. These 2-complexes are, in a sense, hyperbolic
relative to their flats. More precisely, we show that several
important properties of Gromov-hyperbolic spaces hold `relative to
flats' in nonpositively curved 2-complexes with the Isolated Flats
Property.
We introduce the Relatively Thin Triangle Property, which states
roughly that the fat part of a geodesic triangle lies near a single
flat. We also introduce the Relative Fellow Traveller Property, which
states that pairs of quasigeodesics with common endpoints fellow
travel relative to flats, in a suitable sense. The main result of this
paper states that in the setting of CAT(0) 2-complexes, the Isolated
Flats Property is equivalent to the Relatively Thin Triangle Property
and is also equivalent to the Relative Fellow Traveller Property.
Keywords.
Word hyperbolic, nonpositive curvature, thin triangles, quasigeodesics, isolated flats
AMS subject classification.
Primary: 20F67.
Secondary: 20F06, 57M20.
DOI: 10.2140/gt.2004.8.205
E-print: arXiv:math.MG/0402231
Submitted to GT on 22 January 2003.
(Revised 12 February 2004.)
Paper accepted 17 December 2003.
Paper published 12 February 2004.
Notes on file formats
G Christopher Hruska
Department of Mathematics, University of Chicago
5734 S University Ave, Chicago, IL 60637, USA
Email: chruska@math.uchicago.edu
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