Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2010-05-01

Journal: TOPOLOGY AND ITS APPLICATIONS

Included Journals: SCIE

Volume: 157

Issue: 7

Page Number: 1188-1194

ISSN: 0166-8641

Key Words: Distance; Heegaard genus; Annulus sum

Abstract: Let M(i) be a compact orientable 3-manifold, and A(i) a non-separating incompressible annulus on partial derivative M(i), i = 1,2. Let h : A(1) -> A(2) be a homeomorphism, and M = M(1) U(h) M(2) 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) U(Si) W(i) with distance d(S(i)) >= 2g(M(i)) + 3 for i = 1.2, then g(M) = g(M(1)) + g(M(2)). Moreover, if g(F(i)) >= 2, i = 1.2, then the minimal Heegaard splitting of M is unique. (C) 2010 Elsevier B.V. All rights reserved.