Homology of Gaussian groups

We describe new combinatorial methods for constructing an explicit free resolution of Z by ZG-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...

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Bibliographic Details
Main Authors Dehornoy, Patrick, Lafont, Yves
Format Journal Article
LanguageEnglish
Published 21.11.2001
Subjects
Mathematics - Group Theory
Mathematics - K-Theory and Homology
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Summary:We describe new combinatorial methods for constructing an explicit free resolution of Z by ZG-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 groups of finite Coxeter type, so, as a corollary, they give new ways of computing the homology of these groups.
DOI:10.48550/arxiv.math/0111231