English

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

R2 v1 2026-06-21T18:22:43.837Z