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...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.展开更多
基金Supported in part by (Grant No.12071051)of NSFCthe Fundamental Research Funds (Grant No.DUT21LAB302)for the Central Universities。
文摘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.
