Core curves of triangulated solid tori
Geometric Topology
2011-06-16 v1
Abstract
We show that in any triangulation of a solid torus, there is a pre-core curve that lies in the 2-skeleton and that intersects the interior of each face in at most 10 straight arcs. By definition, a pre-core curve is a simple closed curve that becomes a core curve when a collar is attached to the boundary of the solid torus. This theorem imposes restrictions on the possible Riemannian metrics on a solid torus. It also has applications in knot theory.
Keywords
Cite
@article{arxiv.1106.2934,
title = {Core curves of triangulated solid tori},
author = {Marc Lackenby},
journal= {arXiv preprint arXiv:1106.2934},
year = {2011}
}
Comments
26 pages, 10 figures