Open Collections

Description

Given a sufficiently nice embedded space curve, we can thicken it into a physical rope. A pair of physical configurations is Gordian if there is no physical isotopy that takes one to the other. It is an (old) open problem to describe a Gordian unknot. We will explore some special configurations of physical links by considering extrusion along with various packing constraints. This is a dual perspective to the topological sweep-out procedure Coward and Hass used to first describe a Gordian split link. There are some advantages that appear with our shifted view; we trade a general statement about knots and surfaces for tighter area bounds and rigidity, severely constraining the character of certain physical isotopies. In the end, we claim this is sufficient to describe a Gordian Unlink. Related to work with Rob Kusner, Greg Buck.