H'-splittings of Seifert Manifolds with Boundary

It is known that each compact connected orient able 3-manifold M with boundary admits an H’-splitting H1∪FH2,where F is a compact connected orientable surface properly embedded in M and splits M into two handlbodies H_(1) and H_(2).In this paper,we show 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,and 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,and describe a characteristic of some H’-splittings to denote a Seifert 3-manifold with boundary.For a compact connected orientable Seifert manifold M with a semi-bundle structure M_(1)∪_(F)M_(2),we give an upper bound of the genus of the base surface.