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2006 Geodesic knots in cusped hyperbolic 3–manifolds
Sally M Kuhlmann
Algebr. Geom. Topol. 6(5): 2151-2162 (2006). DOI: 10.2140/agt.2006.6.2151

Abstract

We consider the existence of simple closed geodesics or “geodesic knots” in finite volume orientable hyperbolic 3-manifolds. Previous results show that a least one geodesic knot always exists [Bull. London Math. Soc. 31(1) (1999) 81–86], and that certain arithmetic manifolds contain infinitely many geodesic knots [J. Diff. Geom. 38 (1993) 545–558], [Experimental Mathematics 10(3) (2001) 419–436]. In this paper we show that all cusped orientable finite volume hyperbolic 3-manifolds contain infinitely many geodesic knots. Our proof is constructive, and the infinite family of geodesic knots produced approach a limiting infinite simple geodesic in the manifold.

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Sally M Kuhlmann. "Geodesic knots in cusped hyperbolic 3–manifolds." Algebr. Geom. Topol. 6 (5) 2151 - 2162, 2006. https://doi.org/10.2140/agt.2006.6.2151

Information

Received: 21 April 2006; Accepted: 5 September 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1129.53023
MathSciNet: MR2263061
Digital Object Identifier: 10.2140/agt.2006.6.2151

Subjects:
Primary: 53C22, 57N10
Secondary: 30F40, 57M50

Rights: Copyright © 2006 Mathematical Sciences Publishers

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