Handlebody subgroups in a mapping class group

preprint2016arXivOpen access

Abstract

Suppose subgroups A,B<MCG(S)A,B < MCG(S) in the mapping class group of a closed orientable surface SS are given and let ⟨A,B⟩\langle A, B \rangle be the subgroup they generate. We discuss a question by Minsky asking when ⟨A,B⟩≃A∗A∩BB\langle A, B \rangle \simeq A*_{A \cap B} B for handlebody subgroups A,BA,B.

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