## On Simply Knotted Tori in $S^4$

J. Math. Sci. Univ. Tokyo
Vol. 4 (1997), No. 2, Page 279--339.

Shima, Akiko
On Simply Knotted Tori in $S^4$
Let $T$ be a torus in $S^{4}$. If the singular set $Î(T^{*})$ 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 $S^{4}$.