On the distortion of knots on embedded surfaces. (English) Zbl 1227.57013

Pardon, John

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

Summary: 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.

MSC:

57M25	Knots and links in the \(3\)-sphere (MSC2010)
53A04	Curves in Euclidean and related spaces

Keywords:

knot distortion

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