We develop an algorithm of polynomial time complexity to construct the Grushko decomposition of fundamental groups of graphs of free groups with cyclic edge groups. Our methods rely on analysing vertex links of certain CAT(0) square complexes naturally associated with a special class of the above groups. Our main result transforms a one-ended CAT(0) square complex of the above type to one whose vertex links satisfy a strong connectivity condition, as first studied by Brady and Meier.
Nous développons un algorithme polynomial pour construire la décomposition de Grushko du groupe fondamental d’un graphe de groupes libres à sous-groupes d’arêtes cycliques. Notre méthode repose sur l’analyse du link des sommets d’un complexe carré naturellement associé à une classe spéciale des groupes ci-dessus. Notre résultat principal transforme un complexe carré CAT(0) avec un seul bout en un autre dont le link des sommets vérifie une condition de connectivité forte, étudiée pour la première fois par Brady et Meier.
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Keywords: Free splittings, CAT(0) cube complexes, ends of groups, graphs of groups, Grushko decomposition
Suraj Krishna, M S. 1
CC-BY 4.0
@article{AFST_2023_6_32_3_555_0,
author = {Suraj Krishna, M S.},
title = {Vertex links and the {Grushko} decomposition},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {555--576},
year = {2023},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 32},
number = {3},
doi = {10.5802/afst.1744},
language = {en},
url = {https://www.numdam.org/articles/10.5802/afst.1744/}
}
TY - JOUR AU - Suraj Krishna, M S. TI - Vertex links and the Grushko decomposition JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2023 SP - 555 EP - 576 VL - 32 IS - 3 PB - Université Paul Sabatier, Toulouse UR - https://www.numdam.org/articles/10.5802/afst.1744/ DO - 10.5802/afst.1744 LA - en ID - AFST_2023_6_32_3_555_0 ER -
%0 Journal Article %A Suraj Krishna, M S. %T Vertex links and the Grushko decomposition %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2023 %P 555-576 %V 32 %N 3 %I Université Paul Sabatier, Toulouse %U https://www.numdam.org/articles/10.5802/afst.1744/ %R 10.5802/afst.1744 %G en %F AFST_2023_6_32_3_555_0
Suraj Krishna, M S. Vertex links and the Grushko decomposition. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 32 (2023) no. 3, pp. 555-576. doi: 10.5802/afst.1744
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