On the distortion of knots on embedded surfaces

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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.

Original languageEnglish (US)
Pages (from-to)637-646
Number of pages10
JournalAnnals of Mathematics
Volume174
Issue number1
DOIs
StatePublished - Jul 1 2011

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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