Essential surfaces in highly twisted link complements
Geometric Topology
2015-06-24 v2
Abstract
We prove that in the complement of a highly twisted link, all closed, essential, meridionally incompressible surfaces must have high genus. The genus bound is proportional to the number of crossings per twist region. A similar result holds for surfaces with meridional boundary: such a surface either has large negative Euler characteristic, or is an n-punctured sphere visible in the diagram.
Cite
@article{arxiv.1312.5016,
title = {Essential surfaces in highly twisted link complements},
author = {Ryan Blair and David Futer and Maggy Tomova},
journal= {arXiv preprint arXiv:1312.5016},
year = {2015}
}
Comments
17 pages, 11 figures