Distance Two Links
Abstract
In this paper, we characterize all links in the 3-sphere with bridge number at least three that have a bridge sphere of distance two. We show that a link L has a bridge sphere of distance at most two then it falls into at least one of three categories: (1) The exterior of L contains an essential meridional sphere. (2) L can be decomposed as a tangle product of a Montesinos tangle with an essential tangle in a way that respects the bridge surface and either the Montesinos tangle is rational or the essential tangle contains an incompressible, boundary-incompressible annulus. (3) L is obtained by banding from another link L' that has a bridge sphere of the same Euler characteristic as the bridge sphere for L but of distance 0 or 1.
Cite
@article{arxiv.1309.3787,
title = {Distance Two Links},
author = {Ryan Blair and Marion Campisi and Jesse Johnson and Scott A. Taylor and Maggy Tomova},
journal= {arXiv preprint arXiv:1309.3787},
year = {2013}
}
Comments
27 pages, 13 figures