2007/10/08 by Silvia Benvenuti, Benvenuti, Silvia, Riccardo Piergallini +1
Computer Science · Mathematics · #30F60 #57M20 #57M50 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.0710.1483
openalex publication_date 2007/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We exhibit a set of edges (moves) and 2-cells (relations) making the complex of pant decompositions on a surface a simply connected complex. Our construction, unlike the previous ones, keeps the arguments concerning the structural transformations independent from those deriving from the action of the mapping class group. The moves and the relations turn out to be supported in subsurfaces with 3g-3+n=1,2 (where g is the genus and n is the number of boundary components), illustrating in this way the so called Grothendieck principle.