\(H'\)-splittings of Seifert manifolds with boundary
Heegaard splittings of \(3\)-manifolds are an important topic in low dimensional topology, and play an important role in the study of \(3\)-manifolds. \(H'\)-splittings of \(3\)-manifolds are a generalization of Heegaard splittings to \(3\)-manifolds with boundaries. It is known that each compact connected orientable \(3\)-manifold with boundary admits an \(H'\)-splitting. In the paper under review, the authors study \(H'\)-splittings of Seifert manifolds with boundaries, and prove that a non-completely \(L\)-reducible and minimal \(H'\)-splitting surface for a compact connected irreducible orientable anannular Seifert \(3\)-manifold with boundary is horizontal. Also, the authors give a necessary and sufficient condition for an amalgamation of two compact connected orientable \(3\)-manifolds along a compact connected surface to be a Seifert manifold with boundary.
scientific article; zbMATH DE number 7693486