On ■-reducible 3-manifolds Which Admit Complete Surface Systems  

作　　者：Zhao Yan Lei Feng-chun Li Feng-ling 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian,116024 [2]College of Mathematics and Physics,Bohai University,Jinzhou,Liaoning,121013

出　　处：《Communications in Mathematical Research》2017年第3期215-222,共8页数学研究通讯（英文版）

基　　金：The NSF(11329101,11431009,11329101,11471151 and 11401069)of China;the Fundamental Research Funds(DUT16LK40)for the Central Universities

摘　　要：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;.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^3.

关 键 词：complete surface system ?-reducibility Heegaard splitting 

分 类 号：O186.1[理学—数学]