A combination theorem for the twist conjecture for Artin groups

Oli Jones; Giorgio Mangioni; Giovanni Sartori

doi:10.1016/j.jalgebra.2026.04.016

A combination theorem for the twist conjecture for Artin groups

Oli Jones
, Giorgio Mangioni
, Giovanni Sartori

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

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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.

Original language	English
Pages (from-to)	436-476
Number of pages	41
Journal	Journal of Algebra
Volume	701
Early online date	23 Apr 2026
DOIs	https://doi.org/10.1016/j.jalgebra.2026.04.016
Publication status	Published - 1 Sept 2026

Keywords

Artin groups
Bass–Serre theory
Isomorphism problem
Ribbons
Twist conjecture

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2026.04.016Licence: CC BY

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title = "A combination theorem for the twist conjecture for Artin groups",

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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AU - Mangioni, Giorgio

AU - Sartori, Giovanni

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N2 - 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.

AB - 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.

KW - Artin groups

KW - Bass–Serre theory

KW - Isomorphism problem

KW - Ribbons

KW - Twist conjecture

UR - https://www.scopus.com/pages/publications/105037031076

U2 - 10.1016/j.jalgebra.2026.04.016

DO - 10.1016/j.jalgebra.2026.04.016

M3 - Article

SN - 0021-8693

VL - 701

SP - 436

EP - 476

JO - Journal of Algebra

JF - Journal of Algebra

ER -

A combination theorem for the twist conjecture for Artin groups

Abstract

Keywords

ASJC Scopus subject areas

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