On Representing Homology Classes of 4-Manifolds.
On S-Equivalence of Seifert Matrices.
On signatures and a subgroup of a central extension to the mapping class group.
On singular cut-and-pastes in the 3-space with applications to link theory.
In the study of surfaces in 3-manifolds, the so-called ?cut-and-paste? of surfaces is frequently used. In this paper, we generalize this method, in a sense, to singular-surfaces, and as an application, we prove that two collections of singular-disks in the 3-space R3 which span the same trivial link are link-homotopic in the upper-half 4-space R3 [0,8) keeping the link fixed. Throughout the paper, we work in the piecewise linear category, consisting of simplicial complexes and piecewise linear maps....
On slice knots in the complex projective plane.
We investigate the knots in the boundary of the punctured complex projective plane. Our result gives an affirmative answer to a question raised by Suzuki. As an application, we answer to a question by Mathieu.
On stability of Alexander polynomials of knots and links (survey)
We study distribution of the zeros of the Alexander polynomials of knots and links in S³. After a brief introduction of various stabilities of multivariate polynomials, we present recent results on stable Alexander polynomials.
On tensor representations of knot algebras.
On the AJ conjecture for cables of twist knots
We study the AJ conjecture that relates the A-polynomial and the colored Jones polynomial of a knot in S³. We confirm the AJ conjecture for (r,2)-cables of the m-twist knot, for all odd integers r satisfying ⎧ (r+8)(r−8m) > 0 if m > 0, ⎨ ⎩ r(r+8m−4) > 0 if m < 0.
On the Alexander polynomials of alternating two-component links.
On the asymptotic number of plane curves and alternating knots.
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