no. 2
Homology of gaussian groups
Dehornoy, Patrick1; Lafont, Yves2
1 Université de Caen, Laboratoire de Mathématiques Nicolas Oresme, 14032 Caen (France)
2 Institut Mathématique de Luminy, 163 avenue de Luminy, 13288 Marseille Cedex 9 (France)
Annales de l'Institut Fourier, Volume 53 (2003) no. 2, pp. 489-540.

We describe new combinatorial methods for constructing explicit free resolutions of ℤ by ℤG-modules when G is a group of fractions of a monoid where enough lest common multiples exist (“locally Gaussian monoid”), and therefore, for computing the homology of G. Our constructions apply in particular to all Artin-Tits groups of finite Coexter type. Technically, the proofs rely on the properties of least common multiples in a monoid.

Nous décrivons de nouvelles méthodes combinatoires fournissant des résolutions explicites du module trivial par des ℤG-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.

DOI: 10.5802/aif.1951
Classification: 20J06, 18G35, 20M50, 20F36
Keywords: free resolution, finite resolution, homology, contacting homotopy, braid groups, Artin groups
Mot clés : résolution libre, résolution finie, homologie, homotopie de contact, groupes de tresses, groupes d'Artin
Dehornoy, Patrick 1; Lafont, Yves 2

1 Université de Caen, Laboratoire de Mathématiques Nicolas Oresme, 14032 Caen (France)
2 Institut Mathématique de Luminy, 163 avenue de Luminy, 13288 Marseille Cedex 9 (France) 
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Dehornoy, Patrick; Lafont, Yves. Homology of gaussian groups. Annales de l'Institut Fourier, Volume 53 (2003) no. 2, pp. 489-540. doi : 10.5802/aif.1951. https://aif.centre-mersenne.org/articles/10.5802/aif.1951/

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