A Klein bottle whose singular set consists of three disjoint simple closed curves (Q2725560)

The author proves the following Theorem. Let \(F\) be a Klein bottle embedded in \(S^4\smallsetminus \{\infty\}\). If the singular set of the projection of \(F\) into \(\mathbb{R}^3\) consists of at most three disjoint simple closed curves, then \(F\) bounds a solid Klein bottle in \(S^4\), i.e., \(F\) can be moved to the standard Klein bottle by an ambient isotopy of \(S^4\).NEWLINENEWLINENEWLINEA similar result was proved in a previous paper of the author for embedded tori instead of embedded Klein bottles.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00034].