On the distortion of knots on embedded surfaces

John Pardon

doi:10.4007/annals.2011.174.1.21

On the distortion of knots on embedded surfaces

John Pardon

Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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 δ(T_p,q)≥1/160 min(p, q). This answers a 1983 question of Gromov.

Original language	English (US)
Pages (from-to)	637-646
Number of pages	10
Journal	Annals of Mathematics
Volume	174
Issue number	1
DOIs	https://doi.org/10.4007/annals.2011.174.1.21
State	Published - Jul 2011

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.4007/annals.2011.174.1.21

Cite this

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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 Tp,q satisfies δ(Tp,q)≥1/160 min(p, q). This answers a 1983 question of Gromov.",

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On the distortion of knots on embedded surfaces

Abstract

All Science Journal Classification (ASJC) codes

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