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

Author(s): Bang-He Li; Tian-Jun Li
Journal: Proc. Amer. Math. Soc. 135 (2007), 3745-3753.
MSC (2000): Primary 57R40, 57R57; Secondary 57R17
Posted: June 21, 2007
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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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H. Gao & X. Zhao, Minimal genus problem in ruled manifolds, preprint.

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B. H. Li & T. J. Li, Minimal genus smooth embeddings in $ S^2\times S^2$ and $ CP^2\char93 n\overline{CP}^2$ with $ n\leq 8$, Topology 37(1998), 573-594.

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T. J. Li & A. K. Liu, Symplectic structure on ruled surfaces and generalized adjunction formula, Math. Res. Lett. 2(1995), 453-471. MR 1355707 (96m:57052)

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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: 10.1090/S0002-9939-07-08954-X
PII: S 0002-9939(07)08954-X
Received by editor(s): August 3, 2006
Posted: 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
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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