Marc Lackenby
Published 2011-06-15Version 1
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.
Comments: 26 pages, 10 figures
The Classification of Dehn fillings on the outer torus of a 1-bridge braid exterior which produce solid tori
4-dimensional analogues of Dehn's lemma
Spaces of knots in the solid torus, knots in the thickened torus, and irreducible links in the 3-sphere
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