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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On amalgamations of Heegaard splittings with high distance


Authors: Guoqiu Yang and Fengchun Lei
Journal: Proc. Amer. Math. Soc. 137 (2009), 723-731
MSC (2000): Primary 57M99
Published electronically: September 9, 2008
MathSciNet review: 2448595
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Abstract: Let $ M$ be a compact, orientable 3-manifold and $ F$ an essential closed surface which cuts $ M$ into $ M_{1}$ and $ M_{2}$. Suppose that $ M_{i}$ has a Heegaard splitting $ V_{i}\cup_{S_{i}}W_{i}$ with distance $ D{(S_{i})}\geqslant{2g(M_{i})+1}$, $ i=1, 2$. Then $ g(M)=g(M_1)+g(M_2)-g(F)$, and the amalgamation of $ V_{1}\cup_{S_{1}}W_{1}$ and $ V_{2}\cup_{S_{2}}W_{2}$ is the unique minimal Heegaard splitting of $ M$ up to isotopy.


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Additional Information

Guoqiu Yang
Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang Province, People’s Republic of China
Email: gqyang@hit.edu.cn

Fengchun Lei
Affiliation: Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, Liaoning Province, People’s Republic of China
Email: ffcclei@yahoo.com.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09642-1
PII: S 0002-9939(08)09642-1
Keywords: Amalgamation, distance of Heegaard splitting, minimal Heegaard splitting
Received by editor(s): August 6, 2007
Published electronically: September 9, 2008
Additional Notes: The second author is supported in part by a grant (No. 15071034) of NFSC and a grant (No. 893322) of DLUT
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.