Geodesic
Topological geodesics and virtual rigidity
Funar, Louis1 ; Gadgil, Siddhartha2
1Institut Fourier BP74, UMR 5582, Universite de Grenoble I, 38402 Saint-Martin-d’Heres Cedex, France
2Department of Mathematics, SUNY at Stony Brook, Stony Brook NY 11794, USA
Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 369-380
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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.

DOI : 10.2140/agt.2001.1.369
Keywords: topological geodesic, word-hyperbolic group, residually finite, universal cover, virtual rigidity.

Funar, Louis  1   ; Gadgil, Siddhartha  2

1 Institut Fourier BP74, UMR 5582, Universite de Grenoble I, 38402 Saint-Martin-d’Heres Cedex, France
2 Department of Mathematics, SUNY at Stony Brook, Stony Brook NY 11794, USA 
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Funar, Louis; Gadgil, Siddhartha. Topological geodesics and virtual rigidity. Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 369-380. doi: 10.2140/agt.2001.1.369

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