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Dehornoy, Patrick; Lafont, Yves
Homology of gaussian groups. Annales de l'institut Fourier, 53 no. 2 (2003), p. 489-540
Texte intégral djvu | pdf | Analyses MR 1990005 | Zbl 1100.20036
Class. Math.: 20J06, 18G35, 20M50, 20F36

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Résumé

Nous décrivons de nouvelles méthodes combinatoires fournissant des résolutions explicites du module trivial par des ${\Bbb Z} G$-modules libres lorsque $G$ est le groupe de fractions d'un monoïde possédant suffisamment de ppcm («monoïde localement gaussien»), et donc, permettant de calculer l'homologie de $G$. Nos constructions s'appliquent en particulier à tous les groupes d'Artin-Tits de type de Coexeter fini. D'un point de vue technique, les démonstrations reposent sur les propriétés des ppcm dans un monoïde.

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