-covered foliations of hyperbolic 3-manifolds.
En utilisant la méthode du double quantique, nous construisons une -matrice universelle pour la quantification de la superalgèbre de Lie . Nous utilisons ce résultat pour construire un invariant d’entrelacs et nous montrons qu’il est égal à une spécialisation du polynôme de Dubrovnik introduit par Kauffman.
A new algebraic structure on the orbits of dressing transformations of the quasitriangular Poisson Lie groups is provided. This gives the topological interpretation of the link invariants associated with the Weinstein-Xu classical solutions of the quantum Yang-Baxter equation. Some applications to the three-dimensional topological quantum field theories are discussed.
We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the ‘rank vs. Heegaard genus’ conjecture on hyperbolic 3-manifolds is incompatible with the ‘fixed price problem’ in topological dynamics.
We construct a version of rational Symplectic Field Theory for pairs , where is an exact symplectic manifold, where is an exact Lagrangian submanifold with components subdivided into subsets, and where both and have cylindrical ends. The theory associates to a -graded chain complex of vector spaces over , filtered with filtration levels. The corresponding -level spectral sequence is invariant under deformations of and has the following property: if is obtained by joining a...