2015/02/17 by Sarah Koch, Lei Tan, Koch, Sarah +2
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #History and Theory of Mathematics #Mathematics and Applications #math.GT
paper · pdf · doi:10.48550/arxiv.1502.04760
17 pages
arxiv created 2015/02/17 · openalex publication_date 2015/02/17 · arxiv updated 2015/02/18 · openalex created_date 2022/11/24 · openalex updated_date 2026/07/28
Let f:S2→ S2 be an orientation-preserving branched covering map of degree d≥ 2, and let Σ be an oriented Jordan curve passing through the critical values of f. Then Γ:=f-1(Σ) is an oriented graph on the sphere. In a group email discussion in Fall 2010, W. Thurston introduced balanced planar graphs and showed that they combinatorially characterize all such Γ, where f has 2d-2 distinct critical values. We give a detailed account of this discussion, along with some examples and an appendix about Hurwitz numbers.