On the distortion of knots on embedded surfaces

Details On the distortion of knots on embedded surfaces On the distortion of knots on embedded surfaces

2010-10-10

arxiv.org/abs/1010.1972v3

Ann. of Math. (2) 174 (2011), no. 1, 637--646

Mathematics

Geometric Topology

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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