Generalized Montesinos knots, tunnels and N-torsion.
Generating series and asymptotics of classical spin networks
We study classical spin networks with group SU. In the first part, using Gaussian integrals, we compute their generating series in the case where the edges are equipped with holonomies; this generalizes Westbury’s formula. In the second part, we use an integral formula for the square of the spin network and perform stationary phase approximation under some non-degeneracy hypothesis. This gives a precise asymptotic behavior when the labels are rescaled by a constant going to infinity.
Genus two 3-manifolds are built from handle number one pieces.
Geodesic surfaces in knot complements.
Geometric orbifolds.
An orbifold is a topological space which ?locally looks like? the orbit space of a properly discontinuous group action on a manifold. After a brief review of basic concepts, we consider the special case 3-dimensional orbifolds of the form GammaM, where M is a simply-connected 3-dimensional homogeneous space corresponding to one of Thurston?s eight geometries, and where Gamma < Isom(M) acts properly discontinuously. A general description of these geometric orbifolds is given and the closed...
Geometry and topology of -covered foliations.
Graphs and projective planes in 3-manifolds.
Group actions on fibered three-manifolds.
Group negative curvature for 3-manifolds with genuine laminations.
Groupes fondamentaux des variétés de dimension et algèbres d’opérateurs
Nous proposons une caractérisation géométrique des variétés de dimension ayant des groupes fondamentaux dont toutes les classes de conjugaison autres que sont infinies, c’est-à-dire dont les algèbres de von Neumann sont des facteurs de type : ce sont essentiellement les -variétés à groupes fondamentaux infinis qui n’admettent pas de fibration de Seifert. Autrement dit et plus précisément, soient une -variété connexe compacte et son groupe fondamental, qu’on suppose être infini et avec...
Groups acting on cube complexes.
Group-theoretic conditions under which closed aspherical manifolds are covered by Euclidean space
Hass, Rubinstein, and Scott showed that every closed aspherical (irreducible) 3-manifold whose fundamental group contains the fundamental group of a closed aspherical surface, is covered by Euclidean space. This theorem does not generalize to higher dimensions. However, we provide geometric tools with which variations of this theorem can be proved in all dimensions.