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Indexed by:期刊论文

Date of Publication:2010-06-15

Journal:TOPOLOGY AND ITS APPLICATIONS

Included Journals:SCIE

Volume:157

Issue:9

Page Number:1593-1601

ISSN No.:0166-8641

Key Words:Heegaard distance and genus; (Self) surface sum; Weakly incompressible surfaces

Abstract:Let M be a compact orientable 3-manifold, and let F be a separating (resp. non-separating) incompressible surface in M which cuts M into two 3-manifolds M(1) and M(2) (resp. a manifold M(1)). Then M is called the surface sum (resp. self surface sum) of M(1) and M(2) (resp. M(1)) along F, denoted by M = M(1) boolean OR(F) M(2) (resp. M = M(1) boolean OR(F)). In this paper, we will study how g(M) is related to chi(F), g(M(1)) and g(M(2)) when both M(1) and M(2) have high distance Heegaard splittings. (C) 2010 Elsevier B.V. All rights reserved.