Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-06-15

Journal: TOPOLOGY AND ITS APPLICATIONS

Included Journals: Scopus、SCIE

Volume: 242

Page Number: 33-42

ISSN: 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.