Quotients of the mapping class group by power subgroups
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].
Domaines
Topologie géométrique [math.GT]Origine | Fichiers produits par l'(les) auteur(s) |
---|