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Patrick Dehornoy; Yves Lafont
Homology of gaussian groups
(Homologie des groupes gaussiens)
Annales de l'institut Fourier, 53 no. 2 (2003), p. 489-540, doi: 10.5802/aif.1951
Article PDF | Reviews MR 1990005 | Zbl 1100.20036 | 1 citation in Cedram
Class. Math.: 20J06, 18G35, 20M50, 20F36
Keywords: free resolution, finite resolution, homology, contacting homotopy, braid groups, Artin groups

Résumé - Abstract

We describe new combinatorial methods for constructing explicit free resolutions of ${\Bbb Z}$ by ${\Bbb Z}G$-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.

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