# zbMATH — the first resource for mathematics

Closed geodesics in a hyperbolic manifold, viewed as knots. (Les géodésiques fermées d’une variété hyperbolique en tant que nœuds.) (French) Zbl 1049.57007
Komori, Y. (ed.) et al., Kleinian groups and hyperbolic 3-manifolds. Proceedings of the Warwick workshop, Warwick, UK, September 11–14, 2001. Cambridge: Cambridge University Press (ISBN 0-521-54013-5/pbk). Lond. Math. Soc. Lect. Note Ser. 299, 95-104 (2003).
Summary: The goal of this note is to complete some arguments given in [J. P. Otal, C. R. Acad. Sci., Paris, Ser. I 320, No. 7, 847–852 (1995; Zbl 0840.57008)], in particular in Theorem A of that paper which stated that the closed geodesics which are sufficiently short in a hyperbolic 3-manifold homotopy equivalent to a closed surface are “unknotted”. We will consider also more general hyperbolic 3-manifolds, and give a condition on the Nielsen core of such a manifold insuring that a closed geodesic be unknotted.
For the entire collection see [Zbl 1031.30002].

##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010) 57M50 General geometric structures on low-dimensional manifolds 57N10 Topology of general $$3$$-manifolds (MSC2010) 53C22 Geodesics in global differential geometry
##### Keywords:
hyperbolic 3-manifold; unknotted