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Indexed by:期刊论文

Date of Publication:2018-03-15

Journal:TOPOLOGY AND ITS APPLICATIONS

Included Journals:SCIE、Scopus

Volume:237

Page Number:1-6

ISSN No.: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.