We describe new combinatorial methods for constructing explicit free resolutions of by -modules when is a group of fractions of a monoid where enough lest common multiples exist ("locally Gaussian monoid"), and therefore, for computing the homology of . 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 -modules libres lorsque est le groupe de fractions d’un monoïde possédant suffisamment de ppcm ("monoïde localement gaussien"), et donc, permettant de calculer l’homologie de . 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.
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}, pages = {489--540}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {2}, year = {2003}, doi = {10.5802/aif.1951}, mrnumber = {1990005}, zbl = {1100.20036}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1951/} }
TY - JOUR TI - Homology of gaussian groups JO - Annales de l'Institut Fourier PY - 2003 DA - 2003/// SP - 489 EP - 540 VL - 53 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1951/ UR - https://www.ams.org/mathscinet-getitem?mr=1990005 UR - https://zbmath.org/?q=an%3A1100.20036 UR - https://doi.org/10.5802/aif.1951 DO - 10.5802/aif.1951 LA - en ID - AIF_2003__53_2_489_0 ER -
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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