On Heegaard Splittings with Finitely Many Pairs of Disjoint Compression Disks  

作　　者：Qiang E Zhiyan ZHANG 

机构地区：[1]School of Science,Dalian Maritime University,Liaoning 116033,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2023年第4期496-504,共9页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11671064)。

摘　　要：Suppose V∪S W is a genus-g weakly reducible Heegaard splitting of a closed 3-manifold with finitely many pairs of disjoint compression disks on distinct sides up to isotopy and g>2.We show V∪_(S) W admits an untelescoping:(V_(1)∪_(S1) W_(1))∪F(W_(2)∪_(S2) V_(2))such that Wi has a unique separating compressing disk and d(S_(i))≥2,for i=1,2.If there exist more than one but finitely many pairs of disjoint compression disks,at least one of d(S_(i))is 2 and S is a critical Heegaard surface.

关 键 词：3-manifolds Heegaard splitting weakly reducible critical surfaces 

分 类 号：O186.11[理学—数学]