an:02066312
Zbl 1049.57007
Otal, Jean-Pierre
Closed geodesics in a hyperbolic manifold, viewed as knots
FR
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).
2003
a
57M25 57M50 57N10 53C22
hyperbolic 3-manifold; unknotted
Summary: The goal of this note is to complete some arguments given in [\textit{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].
0840.57008