Abstract
It is a consequence of theorems of Gordon-Reid [J. Knot Theory Ram. 4 (1995) 389–409] and Thompson [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 [Bull. Fac. Eng. Takushoku Univ. 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.
Citation
Hiroshi Goda. Martin Scharlemann. Abigail Thompson. "Levelling an unknotting tunnel." Geom. Topol. 4 (1) 243 - 275, 2000. https://doi.org/10.2140/gt.2000.4.243
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