On the distortion of knots on embedded surfaces

Pages 637-646 from Volume 174 (2011), Issue 1 by John Pardon

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

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Keywords
DOI
http://doi.org/10.4007/annals.2011.174.1.21
MR
2811613
zbMATH
1227.57013
Milestones
Received: 20 December 2010
Revised: 16 February 2011
Accepted: 27 April 2011
Published online: 1 July 2011

Authors

John Pardon

Department of Mathematics
Princeton University
Princeton, NJ 08544