Minimal classifying-space dimension conjecture for virtual Artin groups

Let Γ\Gamma be a Coxeter graph, and let clf(Γ)\mathfrak{cl}^f(\Gamma) denote the spherical clique number of Γ\Gamma, namely the number of vertices in a maximal spherical clique. A cocompact model of classifying space for proper actions is a cocompact model for the classifying space for proper actions of a group. Minimal classifying-space dimension conjecture. The virtual Artin group VA[Γ]\mathrm{VA}[\Gamma] admits a cocompact model of classifying space for proper actions of dimension clf(Γ)\mathfrak{cl}^f(\Gamma). The conjecture proposes the analogue, for virtual Artin groups with torsion, of the minimal-dimensional Salvetti model expected for classical Artin groups; no general resolution is stated in the source.

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Primary source

Federica Gavazzi and Alexandre Martin, “A Deligne complex for virtual Artin groups”, arXiv:2607.24367 (2026).

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