A Seifert algorithm for knotted surfaces (Q1925114)

It is well known that any knot in \(\mathbb{R}^{3}\) bounds an orientable surface. The algorithm to construct it from a plane projection is called the Seifert algorithm. A similar algorithm to construct a \(3\)-manifold bounding a given surface in \(\mathbb{R}^{4}\) is introduced in the paper under review. It uses generically immersed projections to \(\mathbb{R}^{3}\) and generalizes the algorithm given by \textit{C. A. Giller} [Ill. J. Math. 26, 591-631 (1982; Zbl 0485.57013)] which can only apply to projections without triple points. As an application the authors describe how to obtain Heegaard diagrams of the bounding \(3\)-manifolds.