Pour tout nous décrivons tous les endomophismes du groupe de tresses et de son sous-groupe dérivé ainsi que tous les homomorphismes . Ces résultats ne sont nouveaux que pour petits parce que les endomorphismes de sont déjà décrits par Castel pour et les homomorphismes ainsi que les endomorphismes de sont décrits par Kordek et Margalit pour . Nous utilisons des approches très différentes pour et pour .
For any , we describe all endomorphisms of the braid group and of its commutator subgroup , as well as all homomorphisms . These results are new only for small because endomorphisms of are already described by Castel for , and homomorphisms and endomorphisms of are already described by Kordek and Margalit for . We use very different approaches for and for .
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Stepan Yu. Orevkov 1
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@article{AFST_2024_6_33_1_105_0, author = {Stepan Yu. Orevkov}, title = {Homomorphisms of commutator subgroups of braid groups with small number of strings}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {105--121}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 33}, number = {1}, year = {2024}, doi = {10.5802/afst.1763}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1763/} }
TY - JOUR AU - Stepan Yu. Orevkov TI - Homomorphisms of commutator subgroups of braid groups with small number of strings JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2024 SP - 105 EP - 121 VL - 33 IS - 1 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1763/ DO - 10.5802/afst.1763 LA - en ID - AFST_2024_6_33_1_105_0 ER -
%0 Journal Article %A Stepan Yu. Orevkov %T Homomorphisms of commutator subgroups of braid groups with small number of strings %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2024 %P 105-121 %V 33 %N 1 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1763/ %R 10.5802/afst.1763 %G en %F AFST_2024_6_33_1_105_0
Stepan Yu. Orevkov. Homomorphisms of commutator subgroups of braid groups with small number of strings. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 1, pp. 105-121. doi : 10.5802/afst.1763. https://afst.centre-mersenne.org/articles/10.5802/afst.1763/
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