Normal-subgroup automorphism dichotomy conjecture

Let SgS_g be a closed orientable surface and let NN be a normal subgroup of Mod(Sg)\operatorname{Mod}(S_g). Normal-subgroup automorphism dichotomy conjecture. Either

Aut(N)Mod±(Sg),\operatorname{Aut}(N)\cong \operatorname{Mod}^{\pm}(S_g),

or NN is isomorphic to a right-angled Artin group. The source gives examples motivating this dichotomy but no proof of the general assertion.

Sources & referencesView supporting material

Primary source

Dan Margalit, “Problems, Questions, and Conjectures about Mapping Class Groups”, arXiv:1806.08773 (2018).

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