A combination theorem for the twist conjecture for Artin groups

TL;DR

This paper reduces a strong version of the twist conjecture for Artin groups to a simpler case, providing new examples and insights into the isomorphism problem, and proves a related combination result.

Contribution

It simplifies the twist conjecture for Artin groups by reducing it to graphs without separating vertices, introducing new examples and a ribbon property combination result.

Findings

Reduced the twist conjecture to graphs with no separating vertices.

Provided new examples of Artin groups satisfying the conjecture.

Proved a combination result for the ribbon property.

Abstract

We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the isomorphism problem for Artin groups. Along the way we also prove a combination result for the ribbon property for vertices.