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Incompressible surfaces in handlebodies and closed 3-manifolds of Heegaard genus 2


Author: Ruifeng Qiu
Journal: Proc. Amer. Math. Soc. 128 (2000), 3091-3097
MSC (2000): Primary 57N10
DOI: https://doi.org/10.1090/S0002-9939-00-05360-0
Published electronically: May 2, 2000
MathSciNet review: 1664371
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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 [Enhancements On Off] (What's this?)

  • [1] C. Gordon and R. Litherland, Incompressible planar surfaces in 3-manifolds, Topology and its Appl. 18(1984), 121-144. MR 86e:57013
  • [2] J. Hempel, 3-manifolds, Ann. of Math. Studies 86. Princeton Univ. Press, Princeton, New Jersey, 1976. MR 54:3702
  • [3] W. Jaco, Lectures on 3-manifold Topology, Published by Amer. Math. Soc., Providence, Rhode Island, 1980. MR 81k:57009
  • [4] W. Jaco, Adding a 2-handle to a 3-manifold, An application to Property R, Proc. A. M. S. 92(1984), 288-292. MR 86b:57006
  • [5] M. Scharlemann and Y-Q Wu, Hyperbolic manifold and degenerating handle additions, J. Austral. Math. Soc. (series A) 55(1993), 72-89. MR 94e:57019
  • [6] Y-Q Wu, Incompressibility of surfaces in syrgered 3-manifolds, Topology 31(1992), 271-280. MR 94e:57027

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Additional Information

Ruifeng Qiu
Affiliation: Department of Mathematics, Jilin University, Changchun 130023, People’s Republic of China
Email: qrf@mail_jlu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-00-05360-0
Keywords: Heegaard genus, incompressible surface
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
Article copyright: © Copyright 2000 American Mathematical Society

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