2013/07/27 by Samuel J. Taylor, Taylor, Samuel J., Alexander Zupan +1 · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1307.7268
openalex publication_date 2013/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We show that for a surface S, the subgraph of the pants graph determined by fixing a collection of curves that cut S into pairs of pants, once-punctured tori, and four-times-punctured spheres is totally geodesic. The main theorem resolves a special case of a conjecture made by Aramayona, Parlier, and Shackleton and has the implication that an embedded product of Farey graphs in any pants graph is totally geodesic. In addition, we show that a pants graph contains a convex n-flat if and only if it contains an n-quasi-flat.