On the distortion of knots on embedded surfaces

Abstract

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 $\delta (T_{p,q})>\frac{1}{160}\min (p,q)$. This answers a 1983 question of Gromov.

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