The polyhedral tree complex

@article{Dougherty2022ThePT,
  title={The polyhedral tree complex},
  author={Michael Dougherty},
  journal={Combinatorial Theory},
  year={2022}
}
. 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… 

References

SHOWING 1-10 OF 21 REFERENCES

Recognizing topological polynomials by lifting trees

We give a simple geometric algorithm that can be used to determine whether or not a post-critically finite topological polynomial is Thurston equivalent to a polynomial. If it is, the algorithm

Moduli of graphs and automorphisms of free groups

This paper represents the beginning of an a t tempt to transfer, to the study of outer au tomorphisms of free groups, the powerful geometric techniques that were invented by Thurs ton to study

On the self‐linking of knots

This note describes a subcomplex F of the de Rham complex of parametrized knot space, which is combinatorial over a number of universal ‘‘Anomaly Integrals.’’ The self‐linking integrals of

Scattering forms and the positive geometry of kinematics, color and the worldsheet

A bstractThe search for a theory of the S-Matrix over the past five decades has revealed surprising geometric structures underlying scattering amplitudes ranging from the string worldsheet to the

Noncrossing hypertrees

Hypertrees and noncrossing trees are well-established objects in the combinatorics literature, but the hybrid notion of a noncrossing hypertree has received less attention. In this article I

Deformations of Bordered Surfaces and Convex Polytopes

T he moduli space of Riemann surfaces of genus g with nmarked particles is influential in many areas of mathematics and theoretical physics, ranging from quantum cohomology to number theory to fluid

A Space of Cyclohedra

The structure of this aspherical space, coming from blow-ups of hyperplane arrangements, is explored, as well as possibilities of its role in knot theory and mathematical physics are discussed.