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论文类型：期刊论文

发表时间：2016-01-01

发表刊物：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

收录刊物：SCIE

卷号：144

期号：1

页面范围：423-434

ISSN号：0002-9939

摘要：Let M = V boolean OR(S) W be a Heegaard splitting of a 3-manifold M and let F be a component of partial derivative M lying in partial derivative-V. A simple closed curve J in F is said to be distance degenerating if the distance of M-J = V-J boolean OR(S) W is less than the distance of M = V boolean OR(S) W where M-J is the 3-manifold obtained by attaching a 2-handle to M along J. In this paper, we will prove that for a strongly irreducible Heegaard splitting M = V boolean OR(S) W, if V is simple or M = V boolean OR(S) W is locally complicated, then the diameter of the set of distance degenerating curves in F is bounded.