A combination theorem for the twist conjecture for Artin groups

Oli Jones; Giorgio Mangioni; Giovanni Sartori

doi:10.1016/j.jalgebra.2026.04.016

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arXiv · 2507.13971

A combination theorem for the twist conjecture for Artin groups

Oli Jones·Giorgio Mangioni·Giovanni Sartori

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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.

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Oli Jones, Giorgio Mangioni, Giovanni Sartori. 2025-07-18. A combination theorem for the twist conjecture for Artin groups. https://doi.org/10.1016/j.jalgebra.2026.04.016

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