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Indexed by:期刊论文

Date of Publication:2018-06-15

Journal:TOPOLOGY AND ITS APPLICATIONS

Included Journals:SCIE、Scopus

Volume:242

Page Number:33-42

ISSN No.:0166-8641

Key Words:Handle addition; Curve complex; Subsurface projection; Keen Heegaard splitting

Abstract: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.