Bridge Number and the Curve Complex
几何拓扑
2007-05-23 v2
摘要
We show that there are hyperbolic tunnel-number one knots with arbitrarily high bridge number and that "most" tunnel-number one knots are not one-bridge with respect to an unknotted torus. The proof relies on a connection between bridge number and a certain distance in the curve complex of a genus-two surface.
关键词
引用
@article{arxiv.math/0603102,
title = {Bridge Number and the Curve Complex},
author = {Jesse Johnson},
journal= {arXiv preprint arXiv:math/0603102},
year = {2007}
}
备注
13 pages, 3 figures. References have been added and the order of exposition changed slightly