Lifting a generic surface in 3-space to an embedded surface in 4-space
This paper treats the topic of knotted surfaces. It proves a necessary and sufficient condition when a generic surface in 3-space lifts to an embedded surface in 4-space. The given criterion is in terms of so-called black/white orientation (BW orientation). See the paper for the definition of BW orientation. The main result reads as follows: A generic surface in \(\mathbb{R}^3\) lifts to an embedded surface in \(\mathbb{R}^4\) if and only if its double point set admits a BW orientation. In the introduction of the article the author has listed the criteria that have preceded this one.
scientific article; zbMATH DE number 1501774