paper

Involutions of knots that fix unknotting tunnels

arXiv:math/0401421 · doi:10.1142/S0218216507005506

Abstract

Let K be a knot that has an unknotting tunnel tau. We prove that K admits a strong involution that fixes tau pointwise if and only if K is a two-bridge knot and tau its upper or lower tunnel.

9 pages, 3 figures