The Polyhedral Tree Complex
Combinatorics
2024-09-17 v2 Geometric Topology
Abstract
The tree complex is a simplicial complex defined in recent work of Belk, Lanier, Margalit, and Winarski with natural applications to mapping class groups and complex dynamics. In this article, we connect this setting with the study of certain convex polytopes: 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.
Keywords
Cite
@article{arxiv.2201.11185,
title = {The Polyhedral Tree Complex},
author = {Michael Dougherty},
journal= {arXiv preprint arXiv:2201.11185},
year = {2024}
}
Comments
21 pages, 15 figures. To appear in Combinatorial Theory