Nonintegral boundary-slopes exist
Non-isotopic Heegaard splittings of Seifert fibered spaces. With an appendix by R.Weidmann.
Non-slice linear combinations of algebraic knots
We show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup.
Non-Trivial negative links have positive signature.
Non-triviality of the -polynomial for knots in .
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 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.