Normal-subgroup automorphism dichotomy conjecture

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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.

References

Primary source

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

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