20 citations · 48 across the 9 of their papers we have counts for
9 papers
Generic immersions and totally real embeddings
Naohiko Kasuya, Masamichi Takase
We show that, for a closed orientable n-manifold, with n not congruent to 3 modulo 4, the existence of a CR-regular embedding into complex (n-1)-space ensures the existence of a to…
Knots and links of complex tangents
Naohiko Kasuya, Masamichi Takase
It is shown that every knot or link is the set of complex tangents of a 3-sphere smoothly embedded in the three-dimensional complex space. We show in fact that a one-dimensional su…
Regular-equivalence of -knot diagrams and sphere eversions
Masamichi Takase, Kokoro Tanaka
For each diagram of a -knot, we provide a way to construct a new diagram of the same knot such that any sequence of Roseman moves between and necessarily invol…
On a move reducing the genus of a knot diagram
Kenji Daikoku, Keiichi Sakai, Masamichi Takase
For a knot diagram we introduce an operation which does not increase the genus of the diagram and does not change its representing knot type. We also describe a condition for this…
Singular Seifert surfaces and Smale invariants for a family of 3-sphere immersions
Tobias Ekholm, Masamichi Takase
A self-transverse immersion of the 2-sphere into 4-space with algebraic number of self intersection points equal to -n induces an immersion of the circle bundle over the 2-sphere o…
High-codimensional knots spun about manifolds
Dennis Roseman, Masamichi Takase
Using spinning we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere. Consider the 2-torus standardly embedded in the 3-sphere, which is furthe…
The Hopf invariant of a Haefliger knot
Masamichi Takase
We show that Haefliger's differentiable (6,3)-knot bounds, in 6-space, a 4-manifold (a Seifert surface) of arbitrarily prescribed signature. This implies, according to our previous…
Homology 3-spheres in codimension three
Masamichi Takase
For smooth embeddings of an integral homology 3-sphere in the 6-sphere, we define an integer invariant in terms of their Seifert surfaces. Our invariant gives a bijection between t…
Regular homotopy classes of immersions of 3-manifolds into 5-space
Osamu Saeki, András Szűcs, Masamichi Takase
We give geometric formulae which enable us to detect (completely in some cases) the regular homotopy class of an immersion with trivial normal bundle of a closed oriented 3-manifol…