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Abstract Given a non‐positively curved cube complex , we prove that the quotient of defined by a cubical presentation satisfying sufficient non‐metric cubical small‐cancellation conditions is hyperbolic provided that is hyperbolic. This generalises the fact that finitely presented classical small‐cancellation groups are hyperbolic.
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Free, publicly-accessible full text available January 1, 2026
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The Tits Conjecture, proved by Crisp and Paris, states that squares of the standard generators of any Artin group generate an obvious right-angled Artin subgroup. We consider a larger set of elements consisting of all the centers of the irreducible spherical special subgroups of the Artin group, and conjecture that sufficiently large powers of those elements generate an obvious right-angled Artin subgroup. This alleged right-angled Artin subgroup is in some sense as large as possible; its nerve is homeomorphic to the nerve of the ambient Artin group. We verify this conjecture for the class of locally reducible Artin groups, which includes all 2-dimensional Artin groups, and for spherical Artin groups of any type other than 𝐸₆, 𝐸₇, 𝐸₈. We use our results to conclude that certain Artin groups contain hyperbolic surface subgroups, answering questions of Gordon, Long and Reid.more » « less
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