On the distortion of knots on embedded surfaces

Mathematics – Geometric Topology

Scientific paper

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Scientific paper

10.4007/annals.2011.174.1.21

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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