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Article Dans Une Revue Bulletin of the London Mathematical Society Année : 2019

Quotients of the mapping class group by power subgroups

Louis Funar
Javier Aramayona
  • Fonction : Auteur

Résumé

We study the quotient of the mapping class group Modgn of a surface of genus g with n punctures, by the subgroup Modgn[p] generated by the pth powers of Dehn twists. Our first main result is that Modg1/Modg1[p] contains an infinite normal subgroup of infinite index, and in particular is not commensurable to a higher rank lattice, for all but finitely many explicit values of p. Next, we prove that Modg0/Modg0[p] contains a Kahler subgroup of finite index, for every p > 2 coprime with six. Finally, we observe that the existence of finite-index subgroups of Modg0 with infinite abelianization is equivalent to the analogous problem for Modg0/Modg0[p].

Dates et versions

hal-01992036 , version 1 (24-01-2019)

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Louis Funar, Javier Aramayona. Quotients of the mapping class group by power subgroups. Bulletin of the London Mathematical Society, 2019, 51 (3), pp.385-398. ⟨10.1112/blms.12236⟩. ⟨hal-01992036⟩
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