Finite presentability conjecture for symplectic mapping class groups of right-angled Artin groups

Let Γ\Gamma be a graph, let AΓA_\Gamma be its right-angled Artin group, and let (w,Q)(w,Q) be a symplectic structure on AΓA_\Gamma. Write Mod(Γ,w,Q)\mathrm{Mod}(\Gamma,w,Q) for the subgroup of automorphisms preserving this structure. Finite presentability conjecture. For every graph Γ\Gamma with a symplectic structure (w,Q)(w,Q) on AΓA_\Gamma, the group Mod(Γ,w,Q)\mathrm{Mod}(\Gamma,w,Q) is finitely presented.

Theorem-level finite generation is known, and finite presentability holds in the classical mapping class group case; extending the available combinatorial methods to all such groups remains open.

Sources & referencesView supporting material

Primary source

Matthew B. Day, “Symplectic structures on right-angled Artin groups: between the mapping class group and the symplectic group”, arXiv:0807.4801 (2008).

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