KNOTTED SURFACES IN 3-SPACE WITH SIMPLE FOLD PROJECTIONS
Yuki Takahashi · Journal of Knot Theory and Its Ramifications · 2011
We consider a surface embedded in the 3-space. Such a surface is called unknotted if the closures of the complementary regions in the 3-sphere are both handlebodies. In this paper, we give a sufficient condition for a torus in the 3-space to be unknotted by using a projection onto a plane. We also prove that this condition is not sufficient for surfaces of higher genera.