Déchirures de variétés de dimension trois et la conjecture de Nash de rationalité en dimension trois.
Deformation of string topology into homotopy skein modules.
Deforming representations of knot groups in SU(2).
Dehn filling: A survey
In this paper we give a brief survey of the present state of knowledge on exceptional Dehn fillings on 3-manifolds with torus boundary. For our discussion, it is necessary to first give a quick overview of what is presently known, and what is conjectured, about the structure of 3-manifolds. This is done in Section 2. In Section 3 we summarize the known bounds on the distances between various kinds of exceptional Dehn fillings, and compare these with the distances that arise in known examples. In...
Delta link-homotopy on spatial graphs.
We study new equivalence relations in spatial graph theory. We consider natural generalizations of delta link-homotopy on links, which is an equivalence relation generated by delta moves on the same component and ambient isotopies. They are stronger than edge-homotopy and vertex-homotopy on spatial graphs which are natural generalizations of link-homotopy on links. Relationship to existing familiar equivalence relations on spatial graphs are stated, and several invariants are defined by using the...
Description chirurgicale des revêtements triples simples de ramifiés le long d’un entrelacs
Nous présentons un algorithme permettant de convertir une présentation de variété de dimension 3 comme revêtement simple à trois feuillets de la sphère en une présentation de chirurgie.
Detecting fibred links in S3.
Développements récents sur les groupes de tresses. Applications à la topologie et à l'algèbre
Differentiable Motions of Unknotted, Unlinked Circles in 3-Space.
Discrete thickness
We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are deffned on equilateral polygons with n vertices. It will turn out that the smooth ropelength, which is the scale invariant quotient of length divided by thickness, is the Γ-limit of the discrete ropelength for n → ∞, regarding the topology induced by the Sobolev norm ‖ · ‖ W1,∞(S1,ℝd). This result directly implies the convergence of almost minimizers of the discrete energies...
Discriminant d’un germe et quotients de contact dans la résolution de
Divisibility of twisted Alexander polynomials and fibered knots
We prove that Wada’s twisted Alexander polynomial of a knot group associated to any nonabelian -representation is a polynomial. As a corollary, we show that it is always a monic polynomial of degree for a fibered knot of genus .
DNA knotting in spooling like conformations in bacteriophages.
Does the Jones polynomial detect unknottedness?
Dotted links, Heegaard diagrams, and colored graphs for PL 4-manifolds.
The present paper is devoted to establish a connection between the 4-manifold representation method by dotted framed links (or -in the closed case- by Heegaard diagrams) and the so called crystallization theory, which visualizes general PL-manifolds by means of edge-colored graphs.In particular, it is possible to obtain a crystallization of a closed 4-manifold M4 starting from a Heegaard diagram (#m(S1 x S2),ω) and the algorithmicity of the whole process depends on the effective possibility of recognizing...