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论文类型：期刊论文

发表时间：2015-07-01

发表刊物：SCIENCE CHINA-MATHEMATICS

收录刊物：SCIE、Scopus

卷号：58

期号：7

页面范围：1499-1510

ISSN号：1674-7283

关键字：stabilization; Heegaard distance; subsurface projection

摘要：A closed orientable Haken three manifold containing a non separating incompressible closed surface has two canonical Heegaard splittings, which are called self-amalgamation and bilateral self-amalgamation. Heegaard distance introduced by Hempel is a useful index in studying Heegaard splitting. This paper studies the stabilization problem for the bilateral self-amalgamation, and proves that if the distance of bilateral selfamalgamation of a Heegaard splitting is at least 9, then it is unstabilized, weakly reducible and irreducible.