Rotation systems and simple drawings in surfaces

Abstract

Every simple drawing of a graph in the plane naturally induces a rotation system, but it is easy to exhibit a rotation system that does not arise from a simple drawing in the plane. We extend this to all surfaces: for every fixed surface $\Sigma$, there is a rotation system that does not arise from a simple drawing in $\Sigma$.

19 pages, 14 figures, Submitted to the Electronic Journal of Combinatorics