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Zbl 1100.20036
Dehornoy, Patrick; Lafont, Yves
Homology of Gaussian groups. (English)
[J] Ann. Inst. Fourier 53, No. 2, 489-540 (2003). ISSN 0373-0956; ISSN 1777-5310/e

Summary: We describe new combinatorial methods for constructing explicit free resolutions of $\bbfZ$ by $\bbfZ G$-modules when $G$ is a group of fractions of a monoid where enough least 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 Coxeter type. Technically, the proofs rely on the properties of least common multiples in a monoid.

MSC 2000:: *20J05 Homological methods in group theory
20M05 Free semigroups
20F36 Braid groups; Artin groups
20C07 Group rings of infinite groups and their modules (group theory)
20M50 Connections of semigroups with homological algebra

Keywords: free resolutions; finite resolutions; homology; contracting homotopy; braid groups; Artin groups; groups of fractions; Gaussian monoids

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