6 papers · 1 filter
Orthogonal 2-sphere basis of stable 4-sphere
Akio Kawauchi
Every stable 4-sphere is identified with the double branched covering space of a trivial surface-knot space. As a result of Wall, it is known that any two orthogonal bases of every…
Fusion of boundary surface-link and ribbonness
Akio Kawauchi
A boundary surface-link of at least two components in the 4-sphere is proved to be a ribbon surface-link if the surface-link obtained from it by surgery along a local S-nontrivial…
Quasi-ribbon but non-ribbon surface-link of trivial components
Akio Kawauchi
An operation on a surface-link preserving the surface-knot components called a quasi-equivalence is introduced, which induces an equivalence relation on the surface-links. A quasi-…
Free ribbon lemma for surface-link
Akio Kawauchi
A free surface-link is a surface-link whose fundamental group is a free group not necessarily meridian-based. Free ribbon lemma says that every free sphere-link in the 4-sphere is…
Note on surface-link of trivial components
Akio Kawauchi
As a previous result, it has shown that every sphere-link consisting of trivial components is a ribbon sphere-link. In this note, it is shown that for every closed oriented disconn…
Classifying the surface-knot modules
Akio Kawauchi
The th module of a surface-knot of a genus in the 4-sphere is the th integral homology module of the infinite cyclic covering of the surface-knot complement. The reduced…