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6. Relationships to mapping class groups


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      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.

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          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.