On the distortion of knots on embedded surfaces
classification
🧮 math.GT
keywords
distortionknotsanswersbounddeltaembeddedfracgromov
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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 $\delta(T_{p,q})>\frac 1{160}\min(p,q)$. This answers a 1983 question of Gromov.
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