The universal Vassiliev-Kontsevich invariant for framed oriented links
The virtual and universal braids
We study the structure of the virtual braid group. It is shown that the virtual braid group is a semi-direct product of the virtual pure braid group and the symmetric group. Also, it is shown that the virtual pure braid group is a semi-direct product of free groups. From these results we obtain a normal form of words in the virtual braid group. We introduce the concept of a universal braid group. This group contains the classical braid group and has as quotients the singular braid group, virtual...
The virtual Haken conjecture: Experiments and examples.
The volume spectrum of hyperbolic 4-manifolds.
The Whitehead link, the Borromean rings and the knot 946 are universal.
A link L in S3 is universal if every closed, orientable 3-manifold is a covering of S3 branched over L. Thurston [1] proved that universal links exist and he asked if there is a universal knot, and also if the Whitehead link and the Figure-eight knot are universal. In [2], [3] we answered the first question by constructing a universal knot. The purpose of this paper is to prove that the Whitehead link and the Borromean rings, among others, are universal. The question about the Figure-eight knot...
The writhes of a virtual knot
Kauffman introduced a fundamental invariant of a virtual knot called the odd writhe. There are several generalizations of the odd writhe, such as the index polynomial and the odd writhe polynomial. In this paper, we define the n-writhe for each non-zero integer n, which unifies these invariants, and study various properties of the n-writhe.
The Yang-Baxter equation and invariants of links.
The Yokonuma-Temperley-Lieb algebra
We define the Yokonuma-Temperley-Lieb algebra as a quotient of the Yokonuma-Hecke algebra over a two-sided ideal generated by an expression analogous to the one of the classical Temperley-Lieb algebra. The main theorem provides necessary and sufficient conditions for the Markov trace defined on the Yokonuma-Hecke algebra to pass through to the quotient algebra, leading to a sequence of knot invariants which coincide with the Jones polynomial.
Théorie des nœuds et calcul formel
There are infinitely many Lissajous knots.
Thin position for a connected sum of small knots.
Thin presentation of knots and lens spaces.
Three Conjectures of Combinatorial Topology.
Three-manifolds and Kähler groups
We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kähler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kähler compact complex surface is or .
Three-manifolds and the Temperley-Lieb algebra.
Three-manifolds having complexity at most 9.
Tight contact structures and taut foliations.
Tight contact structures on Seifert manifolds over with one singular fibre.
Tight Polyhedral Klein Bottles, Projective Planes, and Möbius Bands.
Tiling systems and homology of lattices in tree products.