Abstract
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 embeddings of trees and show that the tree complex is the barycentric subdivision of a polyhedral cell complex for which the cells are products of associahedra and cyclohedra.Mathematics Subject Classifications: 05C05, 05C10, 20F65, 52B11Keywords: Associahedra, cyclohedra, planar trees, mapping class groups
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