The polyhedral tree complex

  title={The polyhedral tree complex},
  author={Michael Dougherty},
  journal={Combinatorial Theory},
. The tree complex is a simplicial complex defined in recent work of Belk, Lanier, Margalit, and Winarski with applications to mapping class groups and complex dynamics. This article introduces a connection between this setting and the convex polytopes known as associahedra and cyclohedra. Specifically, we describe a characterization of these polytopes using planar em- beddings of trees and show that the tree complex is the barycentric subdivision of a polyhedral cell complex for which the cells… 



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