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论文类型：期刊论文

发表时间：2009-01-01

发表刊物：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

收录刊物：SCIE、Scopus

卷号：137

期号：2

页面范围：723-731

ISSN号：0002-9939

关键字：Amalgamation; distance of Heegaard splitting; minimal Heegaard splitting

摘要：Let M be a compact, orientable 3-manifold and F an essential closed surface which cuts M into M(1) and M(2). Suppose that M(i) has a Heegaard splitting V(i)boolean OR(Si) W(i) with distance D(S(i)) >= 2g(M(i)) + 1, i = 1, 2. Then g(M) = g(M(1)) + g(M(2)) - g(F), and the amalgamation of V(1)boolean OR(S1) W(1) and V(2)boolean OR(S2) W(2) is the unique minimal Heegaard splitting of M up to isotopy.