Geodesic knots in cusped hyperbolic 3-manifolds
Geometric Topology
2013-01-02 v1
Abstract
We consider the existence of simple closed geodesics or "geodesic knots" in finite volume orientable hyperbolic 3-manifolds. Previous results show that at 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.
Cite
@article{arxiv.0906.5469,
title = {Geodesic knots in cusped hyperbolic 3-manifolds},
author = {Sally M Kuhlmann},
journal= {arXiv preprint arXiv:0906.5469},
year = {2013}
}
Comments
This is the version published by Algebraic & Geometric Topology on 19 November 2006