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
Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold BM, and fπ ： π1 （M）→π1 （M） be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the...Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold BM, and fπ ： π1 （M）→π1 （M） be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the rank of the fixed subgroup of fπ, namely, rankFix（fπ） 〈 2rankπ1（M）, which is an analogue of inequalities on surface groups and hyperbolic 3-manifold groups.展开更多
Seifert's conjecture has been solved and other interesting problems in difFerential topology have been discussed. Certain properties of vector fields on S2 and 53 have been achieved while one treats S2 and S3 as s...Seifert's conjecture has been solved and other interesting problems in difFerential topology have been discussed. Certain properties of vector fields on S2 and 53 have been achieved while one treats S2 and S3 as submanifolds of R3 and R4 respectively. The difFerential structure we consider here is the usual one in mathematical analysis.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.
基金Supported by NSFC(Grant No.11201364)"the Fundamental Research Funds for the Central Universities"
文摘Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold BM, and fπ ： π1 （M）→π1 （M） be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the rank of the fixed subgroup of fπ, namely, rankFix（fπ） 〈 2rankπ1（M）, which is an analogue of inequalities on surface groups and hyperbolic 3-manifold groups.
文摘Seifert's conjecture has been solved and other interesting problems in difFerential topology have been discussed. Certain properties of vector fields on S2 and 53 have been achieved while one treats S2 and S3 as submanifolds of R3 and R4 respectively. The difFerential structure we consider here is the usual one in mathematical analysis.
