Geometric subgroups of surface braid groups
Annales de l'Institut Fourier, Volume 49 (1999) no. 2, p. 417-472

Let M be a surface, let N be a subsurface, and let nm be two positive integers. The inclusion of N in M gives rise to a homomorphism from the braid group B n N with n strings on N to the braid group B m M with m strings on M. We first determine necessary and sufficient conditions that this homomorphism is injective, and we characterize the commensurator, the normalizer and the centralizer of π 1 N in π 1 M. Then we calculate the commensurator, the normalizer and the centralizer of B n N in B m M for large surface braid groups.

Soient M une surface, N une sous-surface et nm deux entiers positifs. L’inclusion de N dans M induit un homomorphisme du groupe B n N des tresses à n brins de N dans le groupe B m M des tresses à m brins de M. Nous donnons dans un premier temps des conditions nécessaires et suffisantes pour que cet homomorphisme soit injectif et caractérisons le commensurateur, le normalisateur et le centralisateur de π 1 N dans π 1 M. Ensuite, nous déterminons le commensurateur, le normalisateur et le centralisateur de B n N dans B m M dans les cas où N est un disque et où N est large.

@article{AIF_1999__49_2_417_0,
     author = {Paris, Luis and Rolfsen, Dale},
     title = {Geometric subgroups of surface braid groups},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {49},
     number = {2},
     year = {1999},
     pages = {417-472},
     doi = {10.5802/aif.1680},
     zbl = {0962.20028},
     mrnumber = {2000f:20059},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1999__49_2_417_0}
}
Paris, Luis; Rolfsen, Dale. Geometric subgroups of surface braid groups. Annales de l'Institut Fourier, Volume 49 (1999) no. 2, pp. 417-472. doi : 10.5802/aif.1680. http://www.numdam.org/item/AIF_1999__49_2_417_0/

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