The conjectural dichotomy for normal subgroups of mapping class groups

Let NN be a normal subgroup of either the orientation-preserving mapping class group Mod(Sg)\operatorname{Mod}(S_g) or the extended mapping class group MCG(Sg)\operatorname{MCG}(S_g). Normal-subgroup dichotomy conjecture. Either

AutNMCG(Sg),\operatorname{Aut}N\cong\operatorname{MCG}(S_g),

or NN contains an infinitely generated right-angled Artin group with finite index. This conjectural dichotomy is motivated by the authors' theorem on normal subgroups and known exotic subgroup constructions, but it remains open.

Sources & referencesView supporting material

Primary source

Tara Brendle and Dan Margalit, “Normal subgroups of mapping class groups and the metaconjecture of Ivanov”, arXiv:1710.08929 (2018).

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