Non-triviality of the -polynomial for knots in .
Normal all pseudo-Anosov subgroups of mapping class groups.
Normal-convexity and equations over groups.
Note on the Casson-Gordon Invariant of a Satellite Knot.
Notes on tiled incompressible tori
Let Θ denote the class of essential tori in a closed braid complement which admit a standard tiling in the sense of Birman and Menasco [Birman J.S., Menasco W.W., Special positions for essential tori in link complements, Topology, 1994, 33(3), 525–556]. Moreover, let R denote the class of thin tiled tori in the sense of Ng [Ng K.Y., Essential tori in link complements, J. Knot Theory Ramifications, 1998, 7(2), 205–216]. We define the subclass B ⊂ Θ of typical tiled tori and show that R ⊂ B. We also...
Null k-cobordant links in S3.
Nullification number and flyping conjecture
Numerical application of knot invariants and universality of random knotting
We study universal properties of random knotting by making an extensive use of isotopy invariants of knots. We define knotting probability () by the probability of an N-noded random polygon being topologically equivalent to a given knot K. The question is the following: for a given model of random polygon how the knotting probability changes with respect to the number N of polygonal nodes? Through numerical simulation we see that the knotting probability can be expressed by a simple function of...
Of Torus and Turk's-Head Knots: A Polar Trigonometric Modeling
On 10-crossing knots
On 3-manifold invariants arising from finite-dimensional Hopf algebras.
On 3-Manifolds with Finite Solvable Fundamental Groups.
On 4-fold covering moves.
On a certain move generating link-homology.
On a class of spaces for which the fixed-point property is characterized by homology groups
On a Conjecture of Magnus on the Hurwitz Monodromy Group.
On a covering group theorem and its applications.
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 problem of S. Ulam concerning Cartesian squares of 2-dimensional polyhedra
On a proof of the JSJ theorem.