Paper
Extrinsic systole of Seifert surfaces and distortion of knots
Authors
Sahana Vasudevan
Abstract
In 1983, Gromov introduced the notion of distortion of a knot, and asked if there are knots with arbitrarily large distortion. In 2011, Pardon proved that the distortion of is at least up to a constant factor. We prove that the distortion of is at least up to a constant, independent of . We also prove that any embedding of a minimal genus Seifert surface for in has small extrinsic systole, in the sense that it contains a non-contractible loop with small -diameter relative to the length of the knot. These results are related to combinatorial properties of the monodromy map associated to torus knots.