Topological geodesics and virtual rigidity

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

References

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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

Volume 1, issue 1 (2001)

Louis Funar and Siddhartha Gadgil