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Indexed by:期刊论文

Date of Publication:2009-01-01

Journal:PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

Included Journals:SCIE、Scopus

Volume:137

Issue:2

Page Number:723-731

ISSN No.:0002-9939

Key Words:Amalgamation; distance of Heegaard splitting; minimal Heegaard splitting

Abstract: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.