Our main result is a nontrivial lower bound for the distortion of some specific knots. In particular, we show that the distortion of the torus knot $T_{p,q}$ satisfies $\delta(T_{p,q}) \geq \frac 1{160}\min(p,q)$. This answers a 1983 question of Gromov.
Milestones
Received: 20 December 2010
Revised: 16 February 2011
Accepted: 27 April 2011
Published online: 1 July 2011
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