Many different disk knots with the same exterior.
New link invariants and applications.
On diffeomorphisms over surfaces trivially embedded in the 4-sphere.
On Dihedral Covering Spaces of Knots.
On Knot Modules.
On link maps and their homotopy classification.
On links with one codimension two compontent.
On Representing Homology Classes of 4-Manifolds.
On simple fibered knots in S5 and the existence of decomposable algebraic 3-knots.
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 surface braids of index four with at most two crossings
Let Γ be a 4-chart with at most two crossings. We show that if the closure of the surface braid obtained from Γ is one 2-sphere, then the sphere is a ribbon surface.
On the generalized Massey–Rolfsen invariant for link maps
For and a link map let , define a map by and a (generalized) Massey-Rolfsen invariant to be the homotopy class of . We prove that for a polyhedron K of dimension ≤ m - 2 under certain (weakened metastable) dimension restrictions, α is an onto or a 1 - 1 map from the set of link maps up to link concordance to . If are closed highly homologically connected manifolds of dimension (in particular, homology spheres), then .
On the homotopy classification of pairs of linked maps of manifolds into a linear space
On the Slice Genus of Knots.
Periodicity of Branched Cyclic Covers.
Projections of knots
Quandles and symmetric quandles for higher dimensional knots
A symmetric quandle is a quandle with a good involution. For a knot in ℝ³, a knotted surface in ℝ⁴ or an n-manifold knot in , the knot symmetric quandle is defined. We introduce the notion of a symmetric quandle presentation, and show how to get a presentation of a knot symmetric quandle from a diagram.
Quasipsherical knots with infinitely many ends.
Quelques remarques sur les diagrammes de Heegard en grandes dimensions