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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Complexes galoisiens

Author: Yves Ladegaillerie
Journal: Trans. Amer. Math. Soc. 352 (2000), 1723-1741
MSC (2000): Primary 57Q15, 57N10
Published electronically: October 15, 1999
MathSciNet review: 1675202
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Abstract: We construct special $n$-complexes categories which are the object of a Galois theory. Their topological supports are pseudo-manifolds which are branched coverings of spheres. They are a generalization in every dimension of hypercartes. Every category of Galois $n$-complexes is equivalent to a 2-complexes one. Reducing operations are introduced in dimensions two and three. It leads to a notion of irreducible complex which is used in three-dimensions for a simplified generation of 3-manifolds.

Résumé. On construit des catégories de $n$-complexes simpliciaux particuliers qui sont l'objet d'une théorie galoisienne. Topologiquement, ce sont des pseudo-variétés revêtements ramifiés de sphères. En particulier, ce sont des généralisations des hypercartes aux dimension supérieures. Tout catégorie de $n$-complexes galoisiens est équivalente à une catégorie de 2-complexes. Des opérations de réduction sont introduites en dimensions deux et trois. Elles mènent à une notion de complexe irréductible qui est utilisée en dimension trois pour obtenir une génération simplifiée des 3-variétés.

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Additional Information

Yves Ladegaillerie
Affiliation: Département de Mathématiques, CP 51, Université de Montpellier II, F-34095 Montpellier Cedex 5, France

Keywords: Complexes, coverings, 3-manifolds.
Received by editor(s): December 20, 1997
Received by editor(s) in revised form: January 15, 1998
Published electronically: October 15, 1999
Article copyright: © Copyright 2000 American Mathematical Society

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