Arborescence of positive Thompson links

TL;DR

This paper establishes a connection between positive Thompson group elements and bipartite arborescent tangles, revealing a new geometric interpretation of these algebraic objects.

Contribution

It proves that the links from positive Thompson group elements are exactly the closures of bipartite arborescent tangles, providing a novel geometric perspective.

Findings

Links from positive Thompson group elements are bipartite arborescent tangle closures.

Establishes a correspondence between algebraic and geometric structures.

Enhances understanding of Thompson group $F$ through knot theory.

Abstract

We show that the links associated with positive elements of the Thompson group $F$ coincide with the closures of bipartite arborescent tangles.