In the present paper, we consider a class of compact orientable 3-manifolds with one boundary component, and suppose that the manifolds are ?-reducible and admit complete surface systems. One of our main results says ...In the present paper, we consider a class of compact orientable 3-manifolds with one boundary component, and suppose that the manifolds are ?-reducible and admit complete surface systems. One of our main results says that for a compact orientable, irreducible and ?-reducible 3-manifold M with one boundary component F of genus n > 0 which admits a complete surface system S′, if D is a collection of pairwise disjoint compression disks for ?M, then there exists a complete surface system S for M, which is equivalent to S′, such that D is disjoint from S. We also obtain some properties of such 3-manifolds which can be embedded in S;.展开更多
Let M be a compact connected 3-submanifold of the 3-sphere S^3 with one boundary component F such that there exists a collection of n pairwise disjoint connected orientable surfaces S = {S_1, ···, S_n} ...Let M be a compact connected 3-submanifold of the 3-sphere S^3 with one boundary component F such that there exists a collection of n pairwise disjoint connected orientable surfaces S = {S_1, ···, S_n} properly embedded in M, ?S = {?S_1, ···, ?S_n}is a complete curve system on F. We call S a complete surface system for M, and ?S a complete spanning curve system for M. In the present paper, the authors show that the equivalent classes of complete spanning curve systems for M are unique, that is, any complete spanning curve system for M is equivalent to ?S. As an application of the result,it is shown that the image of the natural homomorphism from the mapping class group M(M) to M(F) is a subgroup of the handlebody subgroup Hn.展开更多
基金The NSF(11329101,11431009,11329101,11471151 and 11401069)of Chinathe Fundamental Research Funds(DUT16LK40)for the Central Universities
文摘In the present paper, we consider a class of compact orientable 3-manifolds with one boundary component, and suppose that the manifolds are ?-reducible and admit complete surface systems. One of our main results says that for a compact orientable, irreducible and ?-reducible 3-manifold M with one boundary component F of genus n > 0 which admits a complete surface system S′, if D is a collection of pairwise disjoint compression disks for ?M, then there exists a complete surface system S for M, which is equivalent to S′, such that D is disjoint from S. We also obtain some properties of such 3-manifolds which can be embedded in S;.
基金supported by the National Natural Science Foundation of China(Nos.11329101,11431009,11329101,11471151,11401069)the grant of the Fundamental Research Funds for the Central Universities(No.DUT14LK12)
文摘Let M be a compact connected 3-submanifold of the 3-sphere S^3 with one boundary component F such that there exists a collection of n pairwise disjoint connected orientable surfaces S = {S_1, ···, S_n} properly embedded in M, ?S = {?S_1, ···, ?S_n}is a complete curve system on F. We call S a complete surface system for M, and ?S a complete spanning curve system for M. In the present paper, the authors show that the equivalent classes of complete spanning curve systems for M are unique, that is, any complete spanning curve system for M is equivalent to ?S. As an application of the result,it is shown that the image of the natural homomorphism from the mapping class group M(M) to M(F) is a subgroup of the handlebody subgroup Hn.
