Abstract

Given a sufficiently nice embedded space curve, we can thicken it into a physical “rope”. A pair of physical configurations might be called “Gordian” if there is no physical isotopy that takes one to the other. It is an (old) open problem to describe a Gordian Unknot: a physical trivial knot that cannot be unknotted.We will examine some features of configurations of physical links and a notion of “extrusion”. This is different from the topological sweep-out perspective that Coward and Hass used to first describe a Gordian split link. Some advantages appear with our shifted view; we trade a general statement about knots and surfaces for packing density bounds and rigidity/transversality statements, severely constraining the character of certain physical isotopies.Related to work with Rob Kusner, Greg Buck.