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Homology of gaussian groups

Patrick Dehornoy, Yves Lafont (2003)

Annales de l’institut Fourier

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.

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