Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-03-15

Journal: TOPOLOGY AND ITS APPLICATIONS

Included Journals: Scopus、SCIE

Volume: 237

Page Number: 1-6

ISSN: 0166-8641

Key Words: Curve complex; Subsurface projection; Keen Heegaard splitting; Unstabilized

Abstract: A Heegaard splitting V-1 boolean OR(s) V-2 is called weakly keen with distance 2 if there are essential separating disks D-i subset of V-i such that a component of V-i-D-i is homeomorphic to F-i x I and there is an unique geodesic {partial derivative D-1, C-0, partial derivative D-2} in C(S) connecting partial derivative D-1 to partial derivative D-2, where C-0 is an essential simple closed curve in S and F-i is a component of partial derivative_V-i for i = 1, 2. In this paper, we give a sufficient condition for the weakly keen Heegaard splittings to be keen. At last, we give a sufficient condition for the self -amalgamation of a weakly keen Heegaard splitting to be unstabilized. (C) 2018 Elsevier B.V. All rights reserved.