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论文类型：期刊论文

发表时间：2018-06-15

发表刊物：TOPOLOGY AND ITS APPLICATIONS

收录刊物：SCIE、Scopus

卷号：242

页面范围：33-42

ISSN号：0166-8641

关键字：Handle addition; Curve complex; Subsurface projection; Keen Heegaard splitting

摘要：Let V boolean OR(s) W be an irreducible Heegaard splitting of M and F a component of partial derivative_V. A simple closed curve J in F is called reducible if M-J = V-J boolean OR(s) W is reducible, where M-J is obtained by attaching a 2-handle to M along J. In this paper, we give a sufficient condition for the diameter of the set of reducible curves in F to be bounded in C(F) for the keen weakly reducible Heegaard splittings. Moreover, an upper bound of the diameter of the set of the reducible curves in F is given under some circumstance for the weakly reducible Heegaard splittings. (C) 2018 Elsevier B.V. All rights reserved.