On the distortion of knots on embedded surfaces


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.


John Pardon

Department of Mathematics
Princeton University
Princeton, NJ 08544