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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On amalgamations of Heegaard splittings with high distance
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by Guoqiu Yang and Fengchun Lei PDF
Proc. Amer. Math. Soc. 137 (2009), 723-731 Request permission

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
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 723-731
  • MSC (2000): Primary 57M99
  • DOI: https://doi.org/10.1090/S0002-9939-08-09642-1
  • MathSciNet review: 2448595