Quantum invariants of links and 3-valent graphs in 3-manifolds
Quelques problèmes d'homotopie et d'isotopie dans les variétés de dimension 3 non irréductibles
Cette note résume une étude sur la comparaison des relations d’homotopie et d’isotopie dans les problèmes suivants : disjonction de deux sphères plongées, plongement de sphères dans une variété de dimension 3 satisfaisant à la conjecture de Poincaré. On mentionne une application aux décompositions en anses des variétés de dimension 4.
Quotients of Coxeter complexes, fundamental groupoids and Regular Graphs.
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.
Realization of simply-connected 4-manifolds with a given boundary.
Realizing automorphisms of the fundamental group of irreducible 3-manifolds containing two-sided projective planes.
...-reducing Dehn surgeries and 1-bridge knots.
Reducing the number of fixed points of some homeomorphisms on nonprime 3-manifolds.
Refined quantum invariants for three-manifolds with structure
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.
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...
Representations of (1,1)-knots
We present two different representations of (1,1)-knots and study some connections between them. The first representation is algebraic: every (1,1)-knot is represented by an element of the pure mapping class group of the twice punctured torus PMCG₂(T). Moreover, there is a surjective map from the kernel of the natural homomorphism Ω:PMCG₂(T) → MCG(T) ≅ SL(2,ℤ), which is a free group of rank two, to the class of all (1,1)-knots in a fixed lens space. The second representation is parametric: every...
Representations of orbifold groups and parabolic bundles.
Representing 3-manifolds by triangulations of . I: A constructive approach.
Representing open 3-manifolds as 3-fold branched coverings.
It is proved that the Freudenthal compactification of an open, connected, oriented 3-manifold is a 3-fold branched covering of S3, and in some cases, a 2-fold branched covering of S3. The branching set is a locally finite disjoint union of strings.
Reshetikhin-Turaev invariants of Seifert 3-manifolds and a rational surgery formula.
Rigidity of cusps in deformations of hyperbolic 3-orbifolds.
Roots and Centralizers of Peripheral Elements in Knot Groups.
Rotation Numbers of Products of Circle Homeomorphisms.