Involving symmetries of Riemann surfaces to a study of the mapping class group.
Jones polynomials, volume and essential knot surfaces: a survey
This paper is a brief overview of recent results by the authors relating colored Jones polynomials to geometric topology. The proofs of these results appear in the papers [18, 19], while this survey focuses on the main ideas and examples.
Kashaev's conjecture and the Chern-Simons invariants of knots and links.
Kleinian groups and the complex of curves.
L2-Topological invariants of 3-manifolds.
La trace du noyau de la chaleur des variétés hyperboliques de dimension 3
Laminar branched surfaces in 3--manifolds.
Large embedded balls and Heegaard genus in negative curvature.
Leafwise smoothing laminations.
Lefschetz fibrations, complex structures and Seifert fibrations on .
Lefschetz fibrations on compact Stein surfaces.
Lengths of simple loops on surfaces with hyperbolic metrics.
Les invariants des 3-variétés périodiques
Soit un entier . Une 3-variété est dite -périodique si et seulement si le groupe cyclique agit semi-librement sur avec un cercle comme l’ensemble des points fixes. Dans cet article, nous utilisons les invariants quantiques pour établir des conditions nécessaires pour qu’une 3-variété soit périodique.
Limit sets of free convergence groups.
Local coordinates for -character varieties of finite-volume hyperbolic 3-manifolds
Given a finite-volume hyperbolic 3-manifold, we compose a lift of the holonomy in with the -dimensional irreducible representation of in . In this paper we give local coordinates of the -character variety around the character of this representation. As a corollary, this representation is isolated among all representations that are unipotent at the cusps.
Local rigidity of aspherical three-manifolds
In this paper we construct, for each aspherical oriented -manifold , a -dimensional class in the -homology of whose norm combined with the Gromov simplicial volume of gives a characterization of those nonzero degree maps from to which are homotopic to a covering map. As an application we characterize those degree one maps which are homotopic to a homeomorphism in term of isometries between the bounded cohomology groups of and .
Manifold structures on abstract regular polytopes.
Maximal tubes under the deformations of 3-dimensional hyperbolic cone-manifolds.
Minoration du spectre des variétés hyperboliques de dimension 3
Soit une variété hyperbolique compacte de dimension 3, de diamètre et de volume . Si on note la -ième valeur propre du laplacien de Hodge-de Rham agissant sur les 1-formes coexactes de , on montre que et , où est une constante ne dépendant que de , et est le nombre de composantes connexes de la partie mince de . En outre, on montre que pour toute 3-variété hyperbolique de volume fini avec cusps, il existe une suite de remplissages compacts de , de diamètre telle que et .
Monopôles de Seiberg-Witten et conjecture de Thom