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

 

Circle-sum and minimal genus surfaces in ruled 4-manifolds


Authors: Bang-He Li and Tian-Jun Li
Journal: Proc. Amer. Math. Soc. 135 (2007), 3745-3753
MSC (2000): Primary 57R40, 57R57; Secondary 57R17
Published electronically: June 21, 2007
MathSciNet review: 2336591
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Abstract: We describe a circle-sum construction of smoothly embedded surface in a smooth 4-manifold. We apply this construction to give a simpler solution of the minimal genus problem for nontrivial $ S^2$ bundles over surfaces. We also treat the case of blow-ups.


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Additional Information

Bang-He Li
Affiliation: Key Laboratory of Mathematical Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
Email: Libh@amss.ac.cn

Tian-Jun Li
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: tjli@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08954-X
PII: S 0002-9939(07)08954-X
Received by editor(s): August 3, 2006
Published electronically: June 21, 2007
Additional Notes: The first author was supported in part by 973 project (2004CB318000).
The second author was supported in part by NSF and the McKnight Foundation
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.