no. 3

Virtual braids and permutations  [ Tresses virtuelles et permutations ]
Annales de l'Institut Fourier, Tome 70 (2020) no. 3, pp. 1341-1362.

Soient VB n le groupe de tresses virtuelles à n brins et 𝔖 n le groupe symétrique de l’ensemble à n éléments. Soient n,m∈ℕ tels que n≥5, m≥2 et n≥m. Nous déterminons tous les homomorphismes de VB n dans 𝔖 m , de 𝔖 n dans VB m et de VB n dans VB m . Comme corollaires nous obtenons que Out(VB n ) est isomorphe à ℤ/2ℤ×ℤ/2ℤ et que VB n est à la fois hopfien et co-hofpien.

Let VB n be the virtual braid group on n strands and let 𝔖 n be the symmetric group on n letters. Let n,m∈ℕ such that n≥5, m≥2 and n≥m. We determine all possible homomorphisms from VB n to 𝔖 m , from 𝔖 n to VB m and from VB n to VB m . As corollaries we get that Out(VB n ) is isomorphic to ℤ/2ℤ×ℤ/2ℤ and that VB n is both, Hopfian and co-Hofpian.

Reçu le : 2018-10-22
Accepté le : 2019-05-21
Publié le : 2020-12-18
DOI : https://doi.org/10.5802/aif.3336
Classification : 20F36,  20E36
Mots clés : groupe de tresses virtuelles, théorie de Bass–Serre, groupe d’Artin, groupe symétrique, produit amalgamé 
@article{AIF_2020__70_3_1341_0,
     author = {Bellingeri, Paolo and Paris, Luis},
     title = {Virtual braids and permutations},
     journal = {Annales de l'Institut Fourier},
     pages = {1341--1362},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {70},
     number = {3},
     year = {2020},
     doi = {10.5802/aif.3336},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2020__70_3_1341_0/}
}
Bellingeri, Paolo; Paris, Luis. Virtual braids and permutations. Annales de l'Institut Fourier, Tome 70 (2020) no. 3, pp. 1341-1362. doi : 10.5802/aif.3336. https://aif.centre-mersenne.org/item/AIF_2020__70_3_1341_0/

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