Homology of gaussian groups
Annales de l'Institut Fourier, Volume 53 (2003) no. 2, p. 489-540
We describe new combinatorial methods for constructing explicit free resolutions of by G-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 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.
DOI : https://doi.org/10.5802/aif.1951
Classification:  20J06,  18G35,  20M50,  20F36
Keywords: free resolution, finite resolution, homology, contacting homotopy, braid groups, Artin groups
@article{AIF_2003__53_2_489_0,
     author = {Dehornoy, Patrick and Lafont, Yves},
     title = {Homology of gaussian groups},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {2},
     year = {2003},
     pages = {489-540},
     doi = {10.5802/aif.1951},
     zbl = {1100.20036},
     mrnumber = {1990005},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2003__53_2_489_0}
}
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. http://www.numdam.org/item/AIF_2003__53_2_489_0/

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