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

 

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
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 $n$.


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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: http://dx.doi.org/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
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