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 Dehn surgeries and 1-bridge knots.
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.
Relations between the Jones and Q polynomials for 2-bridge and 3-braid links.
Relative growth rates of closed geodesics on a surface under varying hyperbolic structures.
Remark on the equisingularity of families of affine plane curves
We give some criteria for the equisingularity of families of affine plane curves.
Remarks on the Cobordism Group of Surface Diffeomorphisms.
Remarks on the history of the classification of knots
Remarques à propos d'un lemme de R.H. Fox, le groupe fondamental d'un revêtement ramifié
Dans cette note, nous reformulons et nous démontrons un lemme dont l’énoncé et la démonstration donnés dans un article de R.H. Fox sur les revêtements ramifiés, comportent un certain nombre d’imprécisions. Nous établissons aussi deux théorèmes qui sont utilisés pour calculer le groupe fondamental de l’antécédent, au sens de Fox, d’un revêtement ramifié lorsque celui-ci est un complexe homogène sans bord de dimension ou une -variété combinatoire sans bord.
Representation of -knots.
Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold
The paper studies the first homology of finite regular branched coverings of a universal Borromean orbifold called B 4,4,4ℍ3. We investigate the irreducible components of the first homology as a representation space of the finite covering transformation group G. This gives information on the first betti number of finite coverings of general 3-manifolds by the universality of B 4,4,4. The main result of the paper is a criterion in terms of the irreducible character whether a given irreducible representation...