Über eine Klasse von Brezelknoten.
Un nouvel invariant pour les sphères d'homologie de dimension trois
Uncountably many wild knots whose cyclic branched covering are S3.
There is a disk in S3 whose interior is PL embedded and whose boundary has a tame Cantor set of locally wild points, such that the n-fold cyclic coverings of S3 branched over the boundary of the disk are all S3. An uncountable set of inequivalent wild knots with these properties is exhibited.
Une autre orientation dans les chaînes et les nœuds et la définition du nombre de nœud
Une famille infinie de noeuds fibrés cobordants à zero et ayant même polynôme d'Alexander.
Une remarque sur certains noeuds de
Unfoldings in Knot Theory.
Unfoldings Knot Theory (Corrigendum).
Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion
For every rational homology 3-sphere with H₁(M,ℤ) = (ℤ/2ℤ)ⁿ we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring) such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root, and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of...
Uniqueness of Symmetries of Knots.
Units of the string link monoids
We show that the map obtained by viewing a geometric (i.e. representative) braid as a string link induces an isomorphism of the n-strand braid group onto the group of units of the n-strand string link monoid.
Unknotting number and knot diagram.
This note is a continuation of a former paper, where we have discussed the unknotting number of knots with respect to knot diagrams. We will show that for every minimum-crossing knot-diagram among all unknotting-number-one two-bridge knot there exist crossings whose exchange yields the trivial knot, if the third Tait conjecture is true.
Unknotting Number, Genus, and Companion Tori.
Unknotting number one knots are prime.
Unknotting tunnels in hyperbolic 3-manifolds.
Unknotting tunnels in two-bridge knot and link complements.
Unraveling the Tangled Complexity of DNA: Combining Mathematical Modeling and Experimental Biology to Understand Replication, Recombination and Repair
How does DNA, the molecule containing genetic information, change its three-dimensional shape during the complex cellular processes of replication, recombination and repair? This is one of the core questions in molecular biology which cannot be answered without help from mathematical modeling. Basic concepts of topology and geometry can be introduced in undergraduate teaching to help students understand counterintuitive complex structural transformations...
Unsolved problems in virtual knot theory and combinatorial knot theory
This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.