For a two-sphere embedded in $\mathbb{R}^4$,how can you check whether or not there is an ambient isotopy to the "standard" 2-sphere (the set of points $(x,y,z,0)$ in $\mathbb{R}^4$ distance 1 from the origin)?
Knot theory was discussed in an intro topology course I took and I'm wondering about further generalizations of the concept. It seems to me that such "knotted" 2-spheres could be created by rotating a knotted arc about a plane in $\mathbb{R}^4$; and knotted tori by rotating a standard knot about a nonintersecting plane. However I cannot think of a way to show which of these constructions, if any, are indeed nonisotopic to their standard counterparts.