It follows from further work of immersed surfaces.
2.
However, the result is not true when the condition " embedded surface " is weakened to " immersed surface ".
3.
A basic result, in contrast to the case of plane curves, is that not every immersed surface lifts to a knotted surface.
4.
Showed that a complete immersed surface in "'R "'3 cannot have constant negative curvature, and show that the curvature cannot be bounded above by a negative constant.
5.
Steiner surfaces, including Boy's surface, the Roman surface and the cross-cap, are models of the real projective plane in "'E "'3, but only the Boy surface is an immersed surface.
6.
In some cases the obstruction is 2-torsion, such as in " Koschorke's example ", which is an immersed surface ( formed from 3 M�bius bands, with a triple point ) that does not lift to a knotted surface, but it has a double cover that does lift . A detailed analysis is given in, while a more recent survey is given in.
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