Homology of gaussian groups
Copyright policy )Homology of gaussian groups
We describe new combinatorial methods for constructing explicit free resolutions of ℤ by 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.
Homological methods in group theory, free resolutions, Free semigroups, generators and relations, word problems, Group rings of infinite groups and their modules (group-theoretic aspects), homology, K-Theory and Homology (math.KT), 20J06, 18G35, 20M50, 20F36, Group Theory (math.GR), Braid groups; Artin groups, Gaussian monoids, Artin groups, contracting homotopy, Mathematics - K-Theory and Homology, FOS: Mathematics, Connections of semigroups with homological algebra and category theory, finite resolutions, braid groups, Mathematics - Group Theory, groups of fractions
Homological methods in group theory, free resolutions, Free semigroups, generators and relations, word problems, Group rings of infinite groups and their modules (group-theoretic aspects), homology, K-Theory and Homology (math.KT), 20J06, 18G35, 20M50, 20F36, Group Theory (math.GR), Braid groups; Artin groups, Gaussian monoids, Artin groups, contracting homotopy, Mathematics - K-Theory and Homology, FOS: Mathematics, Connections of semigroups with homological algebra and category theory, finite resolutions, braid groups, Mathematics - Group Theory, groups of fractions
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