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.
@article{urn:eudml:doc:44449, title = {An unknotting theorem for tori in 4-dimensional spheres.}, journal = {Revista Matem\'atica de la Universidad Complutense de Madrid}, volume = {11}, year = {1998}, pages = {299-309}, zbl = {0919.57018}, mrnumber = {MR1666485}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44449} }
Shima, Akiko. An unknotting theorem for tori in 4-dimensional spheres.. Revista Matemática de la Universidad Complutense de Madrid, Tome 11 (1998) pp. 299-309. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44449/