On the character variety of group representations in SL (2, C) and PSL (2, C).
On the colored Jones polynomials of ribbon links, boundary links and Brunnian links
Habiro gave principal ideals of in which certain linear combinations of the colored Jones polynomials of algebraically-split links take values. The author proved that the same linear combinations for ribbon links, boundary links and Brunnian links are contained in smaller ideals of generated by several elements. In this paper, we prove that these ideals also are principal, each generated by a product of cyclotomic polynomials.
On the complexity of braids
We define a measure of “complexity” of a braid which is natural with respect to both an algebraic and a geometric point of view. Algebraically, we modify the standard notion of the length of a braid by introducing generators , which are Garside-like half-twists involving strings through , and by counting powered generators as instead of simply . The geometrical complexity is some natural measure of the amount of distortion of the times punctured disk caused by a homeomorphism. Our main...
On the Conjugacy Problem for Knot Groups.
On the Goeritz Matrix of a Link.
On the Hantzsche-Wendt Manifold.
On the homotopy classification of pairs of linked maps of manifolds into a linear space
On the impossibility of a generalization of the HOMFLY — Polynomial to Labelled Oriented Graphs
On the Jones polynomial of closed 3-braids.
On the kauffman bracket skein algebra of parallelized surfaces
On the Kauffman polynomial of an adequate link.
On the Kauffman-Harary conjecture for Alexander quandle colorings.
The Kauffman-Harary conjecture is a conjecture for Fox's colorings of alternating knots with prime determinants. We consider a conjecture for Alexander quandle colorings by referring to the Kauffman-Harary conjecture. We prove that this new conjecture is true for twist knots.
On the Mahler measure of Jones polynomials under twisting.
On the minimizers of the Möbius cross energy of links.
On the corresponding to bialgebras
On the placement problem of Reeb components.
On the Polynomials of Periodic Links.
On the residual properties of link groups.
On the Signature of a Link.
On the Signatures of Torus Knots
We study properties of the signature function of the torus knot . First we provide a very elementary proof of the formula for the integral of the signature over the circle. We also obtain a closed formula for the Tristram-Levine signature of a torus knot in terms of Dedekind sums.