A lower bound of genus of amalgamations of Heegaard splittings
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论文类型：期刊论文
发表时间：2009-05-01
发表刊物：MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
收录刊物：SCIE
卷号：146
页面范围：615-623
ISSN号：0305-0041
摘要：In the paper, we give a lower bound on the genus of an amalgamation of two Heegaard splittings V(1) boolean OR(S1) W(1) for M(1) and V(2) boolean OR(S2) W(2) for M(2) along boundary components F(1) and F(2) under some conditions on the distances of the factor Heegaard splittings. A direct consequence is that under some circumstances, g(M) = g(M(1)) + g(M(2)) - g(F) holds, and another is that under some circumstances we have a better lower bound.