Rotation systems and simple drawings in surfaces

2022/07/01 by Paul, Rosna, Salazar, Gelasio, Weinberger, Alexandra
#05C10 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2207.00312

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 Σ, there is a rotation system that does not arise from a simple drawing in Σ.

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