Algebraic and Geometric Topology 1 (2001), paper no. 18, pages 369-380.

Topological geodesics and virtual rigidity

Louis Funar, Siddhartha Gadgil

Abstract. 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.

Keywords. Topological geodesic, word-hyperbolic group, residually finite, universal cover, virtual rigidity.

AMS subject classification. Primary: 57M10, 20F67. Secondary: 57M50.

DOI: 10.2140/agt.2001.1.369

E-print: arXiv:math.GT/0106163

Submitted: 4 April 2001. Accepted: 1 June 2001. Published: 3 June 2001.

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Louis Funar, Siddhartha Gadgil

Institut Fourier BP74, UMR 5582
Universite de Grenoble I
38402 Saint-Martin-d'Heres cedex, France

Department of Mathematics
SUNY at Stony Brook, Stony Brook, NY 11794, USA

Email: funar@fourier.ujf-grenoble.fr, gadgil@math.sunysb.edu

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