-covered foliations of hyperbolic 3-manifolds.
-matrice universelle pour et invariant d’entrelacs associé
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.
Racks and orbits of dressing transformations
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.
Rank gradient, cost of groups and the rank versus Heegaard genus problem
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.
Rapport sur la théorie classique des noeuds (1ère partie)
Rapport sur la théorie classique des nœuds (2ème partie)
Rational knots and a theorem of Kanenobu.
Rational L-groups of Bieberbach groups.
Real algebraic curves and real algebraic functions.
Real deformations and complex topology of plane curve singularities
Realization of primitive branched coverings over closed surfaces following the hurwitz approach
Let V be a closed surface, H⊑π1(V) a subgroup of finite index l and D=[A 1,...,A m] a collection of partitions of a given number d≥2 with positive defect v(D). When does there exist a connected branched covering f:W→V of order d with branch data D and f∶W→V It has been shown by geometric arguments [4] that, for l=1 and a surface V different from the sphere and the projective plane, the corresponding branched covering exists (the data D is realizable) if and only if the data D fulfills the Hurwitz...
Reconstructing Surface Triangulations by Their Intersection Matrices 26 September 2014
The intersection matrix of a simplicial complex has entries equal to the rank of the intersecction of its facets. We prove that this matrix is enough to define up to isomorphism a triangulation of a surface.
Reduced Bers boundaries of Teichmüller spaces
We consider a quotient space of the Bers boundary of Teichmüller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space lying there into a point.This boundary turns out to be independent of the basepoint, and the action of the mapping class group extends continuously to this boundary.This is an affirmative answer to Thurston’s conjecture.He also conjectured that this boundary is homeomorphic to the unmeasured lamination space by the correspondence coming...
Reducing inverse systems of monomorphisms
Reeb vector fields and open book decompositions
We determine parts of the contact homology of certain contact 3-manifolds in the framework of open book decompositions, due to Giroux.We study two cases: when the monodromy map of the compatible open book is periodic and when it is pseudo-Anosov. For an open book with periodic monodromy, we verify the Weinstein conjecture. In the case of an open book with pseudo-Anosov monodromy, suppose the boundary of a page of the open book is connected and the fractional Dehn twist coefficient equals , where...
Reflections of regular maps and Riemann surfaces.
Regenerating hyperbolic cone 3-manifolds from dimension 2
We prove that a closed 3-orbifold that fibers over a hyperbolic polygonal 2-orbifold admits a family of hyperbolic cone structures that are viewed as regenerations of the polygon, provided that the perimeter is minimal.
Regenerating hyperbolic cone structures from Nil.
Regular neighbourhoods and canonical decompositions for groups.
Reidemeister-Turaev torsion modulo one of rational homology threespheres.