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Indexed by:期刊论文

Date of Publication:2014-01-01

Journal:MATHEMATICA SCANDINAVICA

Included Journals:SCIE

Volume:115

Issue:2

Page Number:173-188

ISSN No.:0025-5521

Abstract:Let M-i be a compact orientable 3-manifold, and A(i) an incompressible annulus on a component F-i of delta m(i), i= 1, 2. Suppose A(1) is separating on F-1 and A(2) is non-separating on F-2. Let M be the annulus sum of M-1 and M-2 along A(1) and A(2). In the present paper we show that if M-i has a Heegaard splitting V-i boolean OR (Si) W-i with Heegaard distance d(S-i) >= 2g(M-i) 5 for i = 1, 2, then g(M) = g(M-1) + g(M-2). Moreover, when g(F-2) >= 2, the minimal Heegaard splitting of M is unique up to isotopy.