Levelling an unknotting tunnel
نویسندگان
چکیده
It is a consequence of theorems of Gordon–Reid [4] and Thompson [8] 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 [6], 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. AMS Classification numbers Primary: 57M25
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