Conjecture on normal right-angled Artin subgroups of mapping class groups
Conjecture on normal right-angled Artin subgroups of mapping class groups
Let be an orientable surface, and let denote its mapping class group. Let be a nontrivial normal subgroup of that is isomorphic to a right-angled Artin group. The groups occurring in the authors' construction include the free products
Normal RAAG conjecture. The subgroup is isomorphic to one of the right-angled Artin subgroups of afforded by the authors' construction. In particular, is isomorphic to a free product of the groups
The construction gives examples of normal, non-free, right-angled Artin subgroups, while results for mapping classes with sufficiently small support exclude such groups in that setting. The conjecture seeks to classify all nontrivial normal right-angled Artin subgroups of mapping class groups and remains open.
Sources & referencesView supporting material
Primary source
Matt Clay, Johanna Mangahas and Dan Margalit, “Right-angled Artin groups as normal subgroups of mapping class groups”, arXiv:2001.10587 (2021).
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