Geometric subgroups of surface braid groups

Paris, Luis; Rolfsen, Dale

Annales de l'Institut Fourier, Tome 49 (1999), p. 417-472 / Harvested from Numdam

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Abstract

Soient $M$ une surface, $N$ une sous-surface et $n \leq m$ 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.

Let $M$ be a surface, let $N$ be a subsurface, and let $n \leq m$ 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.

Publié le : 1999-01-01

MR 2000f:20059 | Zbl 0962.20028 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.1680

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     author = {Paris, Luis and Rolfsen, Dale},
     title = {Geometric subgroups of surface braid groups},
     journal = {Annales de l'Institut Fourier},
     volume = {49},
     year = {1999},
     pages = {417-472},
     doi = {10.5802/aif.1680},
     mrnumber = {2000f:20059},
     zbl = {0962.20028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1999__49_2_417_0}
}

Paris, Luis; Rolfsen, Dale. Geometric subgroups of surface braid groups. Annales de l'Institut Fourier, Tome 49 (1999) pp. 417-472. doi : 10.5802/aif.1680. http://gdmltest.u-ga.fr/item/AIF_1999__49_2_417_0/

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