Release Time:2019-03-10  Hits:

Indexed by: Journal Article

Date of Publication: 2009-01-01

Journal: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

Included Journals: Scopus、SCIE

Volume: 137

Issue: 2

Page Number: 723-731

ISSN: 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.