Finite index subgroups of mapping class groups - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2011

Finite index subgroups of mapping class groups

Résumé

Let $g\geq3$ and $n\geq0$, and let ${\mathcal{M}}_{g,n}$ be the mapping class group of a surface of genus $g$ with $n$ boundary components. We prove that ${\mathcal{M}}_{g,n}$ contains a unique subgroup of index $2^{g-1}(2^{g}-1)$ up to conjugation, a unique subgroup of index $2^{g-1}(2^{g}+1)$ up to conjugation, and the other proper subgroups of ${\mathcal{M}}_{g,n}$ are of index greater than $2^{g-1}(2^{g}+1)$. In particular, the minimum index for a proper subgroup of ${\mathcal{M}}_{g,n}$ is $2^{g-1}(2^{g}-1)$.
Fichier principal
Vignette du fichier
MinIndSubV6.pdf (291.51 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00592181 , version 1 (11-05-2011)

Identifiants

Citer

Luis Paris, Jon A Berrick, Volker Gebhardt. Finite index subgroups of mapping class groups. 2011. ⟨hal-00592181⟩
86 Consultations
373 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More