Topological geodesics and virtual rigidity

Details Topological geodesics and virtual rigidity Topological geodesics and virtual rigidity

2001-06-19

arxiv.org/abs/math/0106163v1

Algebr. Geom. Topol. 1 (2001) 369-380

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-18.abs.html

Scientific paper

We introduce the notion of a topological geodesic in a 3-manifold. Under
suitable hypotheses on the fundamental group, for instance word-hyperbolicity,
topological geodesics are shown to have the useful properties of, and play the
same role in several applications as, geodesics in negatively curved spaces.
This permits us to obtain virtual rigidity results for 3-manifolds.

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