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Homomorphisms of commutator subgroups of braid groups with small number of strings
Stepan Yu. Orevkov1
1IMT, Univ. Paul Sabatier, Toulouse, France — Steklov Math. Inst., Moscow, Russia
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 1, pp. 105-121

For any n, we describe all endomorphisms of the braid group B n and of its commutator subgroup B n ′ , as well as all homomorphisms B n ′ →B n . These results are new only for small n because endomorphisms of B n are already described by Castel for n≥6, and homomorphisms B n ′ →B n and endomorphisms of B n ′ are already described by Kordek and Margalit for n≥7. We use very different approaches for n=4 and for n≥5.

Pour tout n nous décrivons tous les endomophismes du groupe de tresses B n et de son sous-groupe dérivé B n ′ ainsi que tous les homomorphismes B n ′ →B n . Ces résultats ne sont nouveaux que pour n petits parce que les endomorphismes de B n sont déjà décrits par Castel pour n≥6 et les homomorphismes B n ′ →B n ainsi que les endomorphismes de B n ′ sont décrits par Kordek et Margalit pour n≥7. Nous utilisons des approches très différentes pour n=4 et pour n≥5.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1763

Stepan Yu. Orevkov  1

1 IMT, Univ. Paul Sabatier, Toulouse, France — Steklov Math. Inst., Moscow, Russia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Stepan Yu. Orevkov. Homomorphisms of commutator subgroups of braid groups with small number of strings. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 1, pp. 105-121. doi: 10.5802/afst.1763
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