Volume 1, issue 1 (2001)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Topological geodesics and virtual rigidity

Louis Funar and Siddhartha Gadgil

Algebraic & Geometric Topology 1 (2001) 369–380

arXiv: math.GT/0106163

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.
Mathematical Subject Classification 2000
Primary: 57M10, 20F67
Secondary: 57M50
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Publication
Received: 4 April 2001
Accepted: 1 June 2001
Published: 3 June 2001
Authors
Louis Funar
Institut Fourier BP74
UMR 5582
Universite de Grenoble I
38402 Saint-Martin-d’Heres Cedex
France
Siddhartha Gadgil
Department of Mathematics
SUNY at Stony Brook
Stony Brook NY 11794
USA