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An unknotting theorem for tori in 4-dimensional spheres.

Akiko Shima — 1998

Revista Matemática Complutense

Let T be a torus in S4 and T* a projection of T. If the singular set Gamma(T*) consists of one disjoint simple closed curve, then T can be moved to the standard position by an ambient isotopy of S4.

On surface braids of index four with at most two crossings

Teruo Nagase; Akiko Shima — 2005

Fundamenta Mathematicae

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.

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