On Simply Knotted Tori in $S^4$

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概要

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• Let $T$ be a torus in $S^{4}$. If the singular set $Γ(T^{*})$ of the projection $T^{*}$ ($\subset S^{3}$) of $T$ consists of three disjoint simple closed curves, then $T$ can be moved to either the standard torus, the spun torus of the trefoil knot $T^{0}(L_{3})$, the twist spun torus of the trefoil knot $T^{3}(L_{3})$, or the torus obtained by attaching a handle to the spun 2-sphere of the trefoil knot, by an ambient isotopy of $S^{4}$.

• 東京大学の論文

著者

• Shima Akiko

  Graduate School Of Mathematical Sciences University Of Tokyo

• Shima Akiko

  Graduate School of Mathematical Sciences, University of Tokyo

関連論文

• A Criterion Beam System for Extensions of a Generic Codimension 1 Immersion from a Closed Manifold into R^n
• Extensions to the Disk of Immersions of the Circle into the Plane
• On Simply Knotted Tori in $S^4$

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