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论文类型：期刊论文

发表时间：2010-06-15

发表刊物：TOPOLOGY AND ITS APPLICATIONS

收录刊物：SCIE

卷号：157

期号：9

页面范围：1593-1601

ISSN号：0166-8641

关键字：Heegaard distance and genus; (Self) surface sum; Weakly incompressible surfaces

摘要：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.