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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Incompressible surfaces in handlebodies and closed 3-manifolds of Heegaard genus 2
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by Ruifeng Qiu
Proc. Amer. Math. Soc. 128 (2000), 3091-3097
DOI: https://doi.org/10.1090/S0002-9939-00-05360-0
Published electronically: May 2, 2000

Abstract:

In this paper, we shall prove that for any integer $n>0$, 1) a handlebody of genus 2 contains a separating incompressible surface of genus $n$, 2) there exists a closed 3-manifold of Heegaard genus $2$ which contains a separating incompressible surface of genus $n$.
References
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Bibliographic Information
  • Ruifeng Qiu
  • Affiliation: Department of Mathematics, Jilin University, Changchun 130023, People’s Republic of China
  • Email: qrf@mail_jlu.edu.cn
  • Received by editor(s): September 20, 1996
  • Received by editor(s) in revised form: November 6, 1998
  • Published electronically: May 2, 2000
  • Additional Notes: This research was supported in part by the National Natural Science Foundation of China.
  • Communicated by: Ronald A. Fintushel
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 3091-3097
  • MSC (2000): Primary 57N10
  • DOI: https://doi.org/10.1090/S0002-9939-00-05360-0
  • MathSciNet review: 1664371