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A lower bound of genus of amalgamations of Heegaard splittings

Published online by Cambridge University Press:  01 May 2009

FENGCHUN LEI  and
GUOQIU YANG
FENGCHUN LEI
Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China. e-mail: ffcclei@yahoo.com.cn
GUOQIU YANG
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China. e-mail: gqyang@hit.edu.cn
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Abstract

In the paper, we give a lower bound on the genus of an amalgamation of two Heegaard splittings V1, ∪S1, W1 for M1 and V2, ∪S2, W2 for M2 along boundary components F1 and F2 under some conditions on the distances of the factor Heegaard splittings. A direct consequence is that under some circumstances, g(M) = g(M1) + g(M2) − g(F) holds, and another is that under some circumstances we have a better lower bound.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 3 , May 2009 , pp. 615 - 623
Copyright
Copyright © Cambridge Philosophical Society 2008

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