7 papers · 1 filter
A spinning construction for virtual 1-knots and 2-knots, and the fiberwise and welded equivalence of virtual 1-knots
Louis H. Kauffman, Eiji Ogasa, Jonathan Schneider
We succeed to generalize spun knots of classical 1-knots to the virtual 1-knot case by using the `spinning construction'. That, is, we prove the following: Let be a spun knot o…
Some properties of ordinary sense slice 1-links: Some answers to the problem (26) of Fox
Eiji Ogasa
We prove that, for any ordinary sense slice 1-link , we can define the Arf invariant and Arf(L)=0. We prove that, for any m-component 1-link L_1, there exists a 3m-component ord…
Nonribbon 2-links all of whose components are trivial knots and some of whose band-sums are nonribbon knots
Eiji Ogasa
There is a nonribbon 2-link all of whose components are trivial 2-knots and one of whose band-sums is a nonribbon 2-knot.
Singularities of the projections of -dimensional knots
Eiji Ogasa
Let n be aninteger>4. There is a smoothly knotted n-dimensional sphere in (n+2)-space such that the singular point set of its projection in (n+1)-space consists of double points an…
Link cobordism and the intersection of slice discs
Eiji Ogasa
It is well-known that all 2-knots are slice. Are all 2-links slice? This is an outstanding open question. In this paper we prove the following: For any 2-component 2-link (J,K)in t…
The intersection of three spheres in a sphere and a new application of the Sato-Levine invariant
Eiji Ogasa
Take transverse immersions f from a disjoint unin of the three 4-spheres , , and into with the following properties: (1) The restriction of to $S^4_…