Convexity properties of Thompson's group F

TL;DR

This paper investigates the geometric properties of Thompson's group F, demonstrating it lacks certain convexity properties with respect to various generating sets, which impacts understanding its geometric group theory structure.

Contribution

The paper establishes that Thompson's group F is not minimally almost convex or almost convex for any generating set within the standard infinite generating set containing x_1.

Findings

F is not minimally almost convex with respect to certain generating sets

F is not almost convex with respect to any generating set within the standard set

Convexity properties of F are negatively characterized in this context

Abstract

We prove that Thompson's group F is not minimally almost convex with respect to any generating set which is a subset of the standard infinite generating set for F and which contains x_1. We use this to show that F is not almost convex with respect to any generating set which is a subset of the standard infinite generating set.