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6. Relationships to mapping class groups

    1. Problem 6.1.

      Which Artin groups embed in the mapping class group of a surface?
          Known: A_n, B_n, D_n, I_2(m), \tilde{A}_n, \tilde{C}_n, RAAGs
        •     In [MR1911508], several Artin groups are shown to be mapping class groups of certain orbifolds.

          Problem 6.2.

          For an Artin group A and orbifold \mathcal O with A \cong MCG(\mathcal O), is there a (reasonably defined) curve complex for \mathcal O which agrees with the complex of irreducible parabolics for A?
              Known for the Braid groups via the standard curve complex

              Cite this as: AimPL: Geometry and topology of Artin groups, available at http://aimpl.org/geomartingp.