Arc distance equals level number
Geometric Topology
2009-01-13 v1
Abstract
A knot K in 1-bridge position with respect to a genus-g Heegaard surface in a 3-manifold can be moved by isotopy through knots in 1-bridge position until it lies in a union of n parallel genus-g surfaces tubed together by n-1 straight tubes, with K intersecting each tube in two arcs connecting the ends. We prove that the minimum n for which this is possible is equal to a Hempel-type distance invariant defined using an arc complex of the two holed genus-g surface
Keywords
Cite
@article{arxiv.0901.1467,
title = {Arc distance equals level number},
author = {Sangbum Cho and Darryl McCullough and Arim Seo},
journal= {arXiv preprint arXiv:0901.1467},
year = {2009}
}
Comments
8 pages, 4 figures, to appear in Proc. Amer. Math. Soc