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Indexed by:期刊论文

Date of Publication:2010-07-01

Journal:SCIENCE CHINA-MATHEMATICS

Included Journals:SCIE

Volume:53

Issue:7

Page Number:1697-1702

ISSN No.:1674-7283

Key Words:amalgamation; essential surface; Heegaard genus

Abstract:Let M (i) be a connected, compact, orientable 3-manifold, F (i) a boundary component of M (i) with g(F (i) ) a (c) 3/4 2, i = 1, 2, and F (1) a parts per thousand S F (2). Let phi: F (1) -> F (2) be a homeomorphism, and M = M (1) a(phi)(a) M (2), F = F (2) = phi(F (1)). Then it is known that g(M) a (c) 1/2 g(M (1))+g(M (2))-g(F). In the present paper, we give a sufficient condition for the genus of an amalgamated 3-manifold not to go down as follows: Suppose that there is no essential surface with boundary (Q (i) , a,Q (i) ) in (M (i) , F (i) ) satisfying chi(Q (i) ) > 3 - 2g(M (i) ), i = 1, 2. Then g(M) = g(M (1)) + g(M (2)) - g(F).