Injective homomorphisms of mapping class groups of non-orientable surfaces

Abstract : Let N be a compact, connected, non-orientable surface of genus ρ with n boundary components, with ρ≥5 and n≥0, and let M(N) be the mapping class group of N. We show that, if G is a finite index subgroup of M(N) and φ:G→M(N) is an injective homomorphism, then there exists f0∈M(N) such that φ(g)=f0gf−10 for all g∈G. We deduce that the abstract commensurator of M(N) coincides with M(N).
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02173806
Contributeur : Imb - Université de Bourgogne <>
Soumis le : jeudi 4 juillet 2019 - 16:46:42
Dernière modification le : mercredi 21 août 2019 - 12:12:02

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Elmas Irmak, Luis Paris. Injective homomorphisms of mapping class groups of non-orientable surfaces. Geometriae Dedicata, Springer Verlag, 2019, 198 (1), pp.149-170. ⟨10.1007/s10711-018-0334-5⟩. ⟨hal-02173806⟩

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