Middle tunnels by splitting
Geometric Topology
2011-08-18 v1
Abstract
For a genus-1 1-bridge knot in the 3-sphere, that is, a (1,1)-knot, a middle tunnel is a tunnel that is not an upper or lower tunnel for some (1,1)-position. Most torus knots have a middle tunnel, and non-torus-knot examples were obtained by Goda, Hayashi, and Ishihara. We generalize their construction and calculate the slope invariants for the resulting middle tunnels. In particular, we obtain the slope sequence of the original example of Goda, Hayashi, and Ishihara.
Keywords
Cite
@article{arxiv.1108.3425,
title = {Middle tunnels by splitting},
author = {Sangbum Cho and Darryl McCullough},
journal= {arXiv preprint arXiv:1108.3425},
year = {2011}
}
Comments
20 pages, 11 figures