Levelling an unknotting tunnel
摘要
It is a consequence of theorems of Gordon-Reid [Tangle decompositions of tunnel number one knots and links, J. Knot Theory and its Ramifications, 4 (1995) 389-409] and Thompson [Thin position and bridge number for knots in the 3-sphere, Topology, 36 (1997) 505-507] that a tunnel number one knot, if put in thin position, will also be in bridge position. We show that in such a thin presentation, the tunnel can be made level so that it lies in a level sphere. This settles a question raised by Morimoto [A note on unknotting tunnels for 2-bridge knots, Bulletin of Faculty of Engineering Takushoku University, 3 (1992) 219-225], who showed that the (now known) classification of unknotting tunnels for 2-bridge knots would follow quickly if it were known that any unknotting tunnel can be made level.
关键词
引用
@article{arxiv.math/9910099,
title = {Levelling an unknotting tunnel},
author = {Hiroshi Goda and Martin Scharlemann and Abigail Thompson},
journal= {arXiv preprint arXiv:math/9910099},
year = {2014}
}
备注
Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol4/paper8.abs.html