Gromov's knot distortion

Gromov's knot distortion

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John Pardon, Princeton University
Fine Hall 314

Gromov defined the distortion of an embedding of $S^1$ into $R^3$ and asked whether every knot could be embedded with distortion less than 100.  There are (many) wild embeddings of $S^1$ into $R^3$ with finite distortion, and this is one reason why bounding the distortion of a given knot class is hard.  I will show how to give a nontrivial lower bound on the distortion of torus knots.  I will also mention some natural conjectures about the distortion, for example that the distortion of the $(2,p)$-torus knots is unbounded.