Of Torus and Turk's-Head Knots: A Polar Trigonometric Modeling
On 10-crossing knots
On 4-fold covering moves.
On a certain move generating link-homology.
On a problem in effective knot theory
The following problem is investigated: «Find an elementary function such that if is a knot diagram with crossings and the corresponding knot is trivial, then there is a sequence of Reidemeister moves that proves triviality such that at each step we have less than crossings». The problem is shown to be equivalent to a problem posed by D. Welsh in [7] and solved by geometrical techniques (normal surfaces).
On a relation between torsion numbers and Alexander matrix of a knot
On Branched Coverings of the 3-Sphere.
On Chern-Simons invariants of geometric 3-manifolds.
On constructions of generalized skein modules
Józef Przytycki introduced skein modules of 3-manifolds and skein deformation initiating algebraic topology based on knots. We discuss the generalized skein modules of Walker, defined by fields and local relations. Some results by Przytycki are proven in a more general setting of fields defined by decorated cell-complexes in manifolds. A construction of skein theory from embedded TQFT-functors is given, and the corresponding background is developed. The possible coloring of fields by elements of...
On Culler-Shalen seminorms and Dehn filling.
On Dihedral Covering Spaces of Knots.
On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number.
On Heegaard Decompositions of Torus Knot Exteriors and Related Seifert Fibre Spaces.
On hyperbolic 3-manifolds obtained by Dehn surgery on links.
On hyperbolic 3-manifolds realizing the maximal distance between toroidal Dehn fillings.
On irregular links at infinity of algebraic plane curves.
On Khovanov's categorification of the Jones polynomial.
On linked Jordan curves in
On links with one codimension two compontent.
On malnormal peripheral subgroups of the fundamental group of a -manifold
Let be a non-trivial knot in the -sphere, its exterior, its group, and its peripheral subgroup. We show that is malnormal in , namely that for any with , unless is in one of the following three classes: torus knots, cable knots, and composite knots; these are exactly the classes for which there exist annuli in attached to which are not boundary parallel (Theorem 1 and Corollary 2). More generally, we characterise malnormal peripheral subgroups in the fundamental group of a...