The infinite associahedron and R.J. Thompson's group T

TL;DR

This paper constructs an infinite associahedron complex, proves its contractibility, and identifies its automorphism group as a semi-direct product involving R.J. Thompson's group T, expanding understanding of infinite combinatorial structures.

Contribution

It introduces an infinite analogue of associahedra, proves its contractibility, and characterizes its automorphism group related to Thompson's group T.

Findings

The complex is contractible.

Automorphism group is a semi-direct product of T and Z/2Z.

Provides new insights into infinite combinatorial structures.

Abstract

In this paper we construct a cellular complex which is an infinite analogue to Stasheff's associahedra. We prove that it is contractible and state that its (combinatorial) automorphism group is isomorphic to a semi-direct product of R.J. Thompson's group $T$ with $\mathbb{Z}/2\mathbb{Z}$.