4 citations · 12 across the 17 of their papers we have counts for
19 papers
The crossing numbers of knots and links via 4D topology
Akio Kawauchi
The diagrams of links (including knots) are characterized in terms of circular rigid disk-chord diagrams of their spun ribbon torus-links in the 4-sphere. As a result, the crossing…
Ribbonness on classical link
Akio Kawauchi
It is shown that if a link in 3-space bounds a proper oriented surface (without closed component) in the upper half 4-space, then the link bounds a proper oriented ribbon surface i…
Kervaire conjecture on weight of group via fundamental group of ribbon sphere-link
Akio Kawauchi
Kervaire conjecture that the weight of the free product of every non-trivial group and the infinite cyclic group is not one is confirmed by confirming Conjecture Z of a knot exteri…
Whitehead aspherical conjecture via ribbon sphere-link
Akio Kawauchi
Whitehead aspherical conjecture says that every connected subcomplex of every aspherical 2-complex is aspherical. By an argument on ribbon sphere-links, it is confirmed that the co…
Ribbonness of Kervaire's sphere-link in homotopy 4-sphere and its consequences to 2-complexes
Akio Kawauchi
M. A. Kervaire showed that every group of deficiency and weight is the fundamental group of a smooth sphere-link of components in a smooth homotopy 4-sphere. In the use…
Classical Poincar{é} conjecture via 4D topology
Akio Kawauchi
The classical Poincar{é} conjecture that every homotopy 3-sphere is diffeomorphic to the 3-sphere is confirmed by Perelman in arXiv papers solving Thurston's program on geometrizat…
Spatial graph as connected sum of a planar graph and a braid
Valeriy G. Bardakov, Akio Kawauchi
In this paper we show that every finite spatial graph is a connected sum of a planar graph, which is a forest, i.e. disjoint union of finite number of trees and a tangle. As a cons…
Smooth homotopy 4-sphere
Akio Kawauchi
Every smooth homotopy 4-sphere is diffeomorphic to the 4-sphere.
Unique diagram of a spatial arc and the knotting probability
Akio Kawauchi
It is shown that the projection image of an oriented spatial arc to any oriented plane is approximated by a unique arc diagram (up to isomorphic arc diagrams) determined from the s…
Ribbonness of a stable-ribbon surface-link, II. General case
Akio Kawauchi
It is shown that any handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link up to equivalences, so that every stable-ribbon surface-link is…
Splitting criteria for a definite 4-manifold with infinite cyclic fundamental group
Akio Kawauchi
Two criteria for a closed connected definite 4-manifold with infinite cyclic fundamental group to be TOP-split are given. One criterion extends a sufficient condition made in a pre…
Triviality of a surface-link with meridian-based free fundamental group
Akio Kawauchi
It is proved that every disconnected surface-link with meridian-based free fundamental group is a trivial (i.e., an unknotted-unlinked) surface-link. This result is a surface-link…
Ribbonness of a stable-ribbon surface-link, I. A stably trivial surface-link
Akio Kawauchi
There is a question asking whether a handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link. This question for the case of a trivial surface…
Biquandle cohomology and state-sum invariants of links and surface-links
Seiichi Kamada, Akio Kawauchi, Jieon Kim +1
In this paper, we discuss the (co)homology theory of biquandles, derived biquandle cocycle invariants for oriented surface-links using broken surface diagrams and how to compute th…
An unknotting index for virtual knots
K. Kaur, S. Kamada, A. Kawauchi +1
In this paper we introduce the notion of an unknotting index for virtual knots. We give some examples of computation by using writhe invariants, and discuss a relationship between…
Presentation of immersed surface-links by marked graph diagrams
Seiichi Kamada, Akio Kawauchi, Jieon Kim +1
It is well known that surface-links in 4-space can be presented by diagrams on the plane of 4-valent spatial graphs with makers on the vertices, called marked graph diagrams. In th…
Polynomial of an oriented surface-link diagram via quantum A_2 invariant
Yewon Joung, Seiichi Kamada, Akio Kawauchi +1
It is known that every surface-link can be presented by a marked graph diagram, and such a diagram presentation is unique up to moves called Yoshikawa moves. G. Kuperberg introduce…
Quantization of the crossing number of a knot diagram
Akio Kawauchi, Ayaka Shimizu
We introduce the warping crossing polynomial of an oriented knot diagram by using the warping degrees of crossing points of the diagram. Given a closed transversely intersected pla…
The first Alexander Z[Z]-modules of surface-links and of virtual links
Akio Kawauchi
We characterize the first Alexander Z[Z]-modules of ribbon surface-links in the 4-sphere fixing the number of components and the total genus, and then the first Alexander Z[Z]-modu…