Géométries modèles de dimension trois
On expose une preuve détaillée de la classification par Thurston des huit géométries modèles de dimension trois.
Geometrization of three manifolds and Perelman's proof.
This is a survey about Thurston’s geometrization conjecture of three manifolds and Perelman’s proof with the Ricci flow. In particular we review the essential contribution of Hamilton as well as some results in topology relevants for the proof.
Geometry and topology of -covered foliations.
Geometry of pseudocharacters.
Gradients de Heegaard sous-logarithmiques d’une variété hyperbolique de dimension trois et fibres virtuelles
J. Maher a montré qu’une variété hyperbolique de dimension compacte sans bord, connexe et orientable fibre virtuellement sur le cercle si et seulement si elle admet une famille infinie de revêtements finis de genre de Heegaard borné. En s’appuyant sur la démonstration de Maher, cet article présente un théorème donnant une condition suffisante pour qu’un revêtement fini d’une variété hyperbolique compacte de dimension contienne une fibre virtuelle, qui s’exprime en fonction du degré du revêtement...
Group negative curvature for 3-manifolds with genuine laminations.
Handlebody splittings of compact 3-manifolds with boundary.
The purpose of this paper is to relate several generalizations of the notion of the Heegaard splitting of a closed 3-manifold to compact, orientable 3-manifolds with nonempty boundary.
Heegaard gradient and virtual fibers.
Heegaard splittings of graph manifolds.
Homotopy and isotopy in dimension three.
Homotopy invariance of higher signatures and -manifold groups
For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable -manifolds, including the “piecewise geometric” ones in the sense of Thurston. In particular, this class, that will be carefully described, is the class of all orientable -manifolds if the Thurston Geometrization Conjecture is true. In fact, for this type of groups, we show that the Baum-Connes Conjecture With Coefficients holds. The...
Hyperbolic cone-manifolds with large cone-angles.
Hyperbolic groups with low-dimensional boundary
Hyperbolic knots and cyclic branched covers.
We collect several results on the determination of hyperbolic knots by means of their cyclic branched covers. We construct examples of knots having two common cyclic branched covers. Finally, we briefiy discuss the problem of determination of hyperbolic links.
Hyperbolic structure on a complement of tori in the 4-sphere.
Hyperbolic volume and mod p homology.
Ideal triangulations of hyperbolic -manifolds
Quello delle triangolazioni geodetiche ideali è un metodo molto potente per costruire strutture iperboliche complete di volume finito su 3-varietà non compatte, ma non è noto se il metodo sia applicabile in generale. È tuttavia noto che esistono triangolazioni ideali parzialmente piatte, ma l'analisi della situazione diviene più ardua sotto diversi aspetti, quando si ha a che fare con tetraedri piatti oltre che veri tetraedri. In particolare, la topologia dello spazio di identificazione può degenerare,...
Inexistence de structures affines sur les fibrés de Seifert.
Intersections in hyperbolic manifolds.
Invariants from triangulations of hyperbolic 3-manifolds.