Thin presentation of knots and lens spaces.
Three-manifolds and the Temperley-Lieb algebra.
Topological Order Complexes and Resolutions of Discriminant Sets
Topological order complexes and resolutions of discriminant sets.
Topologie d'un polynôme de deux variables complexes au voisinage de l'infini
Nous donnons un système complet d’invariants de la classe de conjugaison topologique de polynômes de en dehors d’un compact suffisamment grand dans les deux sens suivants : en tant que feuilletages (en oubliant les valeurs des fibres) et en tant que fonctions. Ces invariants sont donnés par un arbre pondéré, fléché et coloré, obtenu à partir de la résolution des singularités du polynôme sur la droite à l’infini. Nous donnons un critère de régularité pour les valeurs d’un polynôme et une description...
Topology of families of affine plane curves
We determine bifurcation sets of families of affine curves and study the topology of such families.
Torsion in Khovanov homology of semi-adequate links
The goal of this paper is to address A. Shumakovitch's conjecture about the existence of ℤ₂-torsion in Khovanov link homology. We analyze torsion in Khovanov homology of semi-adequate links via chromatic cohomology for graphs, which provides a link between link homology and the well-developed theory of Hochschild homology. In particular, we obtain explicit formulae for torsion and prove that Khovanov homology of semi-adequate links contains ℤ₂-torsion if the corresponding Tait-type graph has a cycle...
Torsion of Khovanov homology
Khovanov homology is a recently introduced invariant of oriented links in ℝ³. It categorifies the Jones polynomial in the sense that the (graded) Euler characteristic of Khovanov homology is a version of the Jones polynomial for links. In this paper we study torsion of Khovanov homology. Based on our calculations, we formulate several conjectures about the torsion and prove weaker versions of the first two of them. In particular, we prove that all non-split alternating links have their integer Khovanov...
Torus knots and Dunwoody manifolds.
Torus knots extremizing the Möbius energy.
Torus knots that cannot be untied by twisting.
We give a necessary condition for a torus knot to be untied by a single twisting. By using this result, we give infinitely many torus knots that cannot be untied by a single twisting.
Total curvature for knotted surfaces.
Trace functions on Iwahori-Hecke algebras
This paper is an expanded version of a talk given at the Banach Center Symposium on Knot Theory in July/August 1995. Its aim is to provide a general survey about trace functions on Iwahori-Hecke algebras associated with finite Coxeter groups. The so-called Markov traces are relevant to knot theory as they can be used to construct invariants of oriented knots and links. We present a classification of Markov traces for the classical types A, B and D.
Traces dans les catégories monoïdales, dualité et catégories monoïdales fibrées
Transversal torus knots.
Turk's-head Knots (Braided Band Knots) a Mathematical Modeling
Twisted Alexander polynomials and surjectivity of a group homomorphism.
Twisted Alexander polynomials of periodic knots.
Twisted quandle homology theory and cocycle knot invariants.
Twisting and unknotting operations.
We define a twisting move, an (n,k)-move, on a link diagram and consider the question as to whether or not any two links are equivalent by this move. Moreover we show that any knot can be trivialized by at most twice twisting operations.