Homology of gaussian groups

Patrick Dehornoy[1]; Yves Lafont[2]

  • [1] Université de Caen, Laboratoire de Mathématiques Nicolas Oresme, 14032 Caen (France)
  • [2] Institut Mathématique de Luminy, 163 avenue de Luminy, 13288 Marseille Cedex 9 (France)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 2, page 489-540
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Dehornoy, Patrick, and Lafont, Yves. "Homology of gaussian groups." Annales de l’institut Fourier 53.2 (2003): 489-540. <http://eudml.org/doc/116044>.

@article{Dehornoy2003,
abstract = {We describe new combinatorial methods for constructing explicit free resolutions of $\{\mathbb \{Z\}\}$ by $\{\mathbb \{Z\}\}G$-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.},
affiliation = {Université de Caen, Laboratoire de Mathématiques Nicolas Oresme, 14032 Caen (France); Institut Mathématique de Luminy, 163 avenue de Luminy, 13288 Marseille Cedex 9 (France)},
author = {Dehornoy, Patrick, Lafont, Yves},
journal = {Annales de l’institut Fourier},
keywords = {free resolution; finite resolution; homology; contacting homotopy; braid groups; Artin groups; free resolutions; finite resolutions; contracting homotopy; groups of fractions; Gaussian monoids},
language = {eng},
number = {2},
pages = {489-540},
publisher = {Association des Annales de l'Institut Fourier},
title = {Homology of gaussian groups},
url = {http://eudml.org/doc/116044},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Dehornoy, Patrick
AU - Lafont, Yves
TI - Homology of gaussian groups
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 2
SP - 489
EP - 540
AB - We describe new combinatorial methods for constructing explicit free resolutions of ${\mathbb {Z}}$ by ${\mathbb {Z}}G$-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.
LA - eng
KW - free resolution; finite resolution; homology; contacting homotopy; braid groups; Artin groups; free resolutions; finite resolutions; contracting homotopy; groups of fractions; Gaussian monoids
UR - http://eudml.org/doc/116044
ER -

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