Spiralling and Folding: The Word View
Marcus Schaefer
School of Computer Science, Telecommunications & Information Systems
DePaul University
We show that for every n there are two simple curves on the torus intersecting at least n times without the two curves folding or spiraling with respect to each other. On the other hand, two simple curves in the plane that intersect at least n times (without creating an empty bigon) must either form a spiral of depth d or a fold of width cn/d, where c only depends on the number of boundary components of the plane. The construction of the two curves on the torus uses train tracks and word equations. Joint work with Eric Sedgwick and Daniel Stefankovic.