Injective Labeled Oriented Trees are Aspherical

TL;DR

This paper proves that injective labeled oriented trees are aspherical, introducing a new relative asphericity test based on Stallings' lemma to establish this property.

Contribution

The paper establishes asphericity for injective labeled oriented trees using a novel relative asphericity test, advancing understanding in geometric group theory.

Findings

Injective labeled oriented trees are aspherical.

A new relative asphericity test is developed.

The proof utilizes Stallings' lemma.

Abstract

A labeled oriented tree is called injective if each generator occurs at most once as an edge label. We show that injective labeled oriented trees are aspherical. The proof relies on a new relative asphericity test based on a lemma of Stallings.