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Incompressible surfaces in handlebodies and closed 3-manifolds of Heegaard genus 2
Author(s):
Ruifeng
Qiu
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3091-3097.
MSC (2000):
Primary 57N10
Posted:
May 2, 2000
MathSciNet review:
1664371
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Abstract:
In this paper, we shall prove that for any integer  , 1) a handlebody of genus 2 contains a separating incompressible surface of genus  , 2) there exists a closed 3-manifold of Heegaard genus  which contains a separating incompressible surface of genus  .
References:
-
- [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:
10.1090/S0002-9939-00-05360-0
PII:
S 0002-9939(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
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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