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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
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  bundles over surfaces. We also treat the case of blow-ups.
References:
-
- 1.
- R. Friedman & J. Morgan, Algebraic surfaces and Seiberg-Witten invariants, J. Algebraic Geom. 6(1997), 445-479. MR 1487223 (99b:32045)
- 2.
- H. Gao & X. Zhao, Minimal genus problem in ruled manifolds, preprint.
- 3.
- B. H. Li & T. J. Li, Symplectic genus, minimal genus and diffeomorphisms, Asian J. Math. 6(2002), 123-144. MR 1902650 (2003c:57027)
- 4.
- B. H. Li & T. J. Li, Minimal genus embeddings of surfaces in
 -bundles over surfaces, Math. Res. Lett. 4(1997), 379-394. MR 1453068 (98h:57062) - 5.
- B. H. Li & T. J. Li, Minimal genus smooth embeddings in
 and  with  , Topology 37(1998), 573-594. - 6.
- 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)
- 7.
- D. Ruberman, The minimal genus of an embedded surface of nonnegative square in a rational surface, Proc. of Gokova Geometry-Topology conference, 1995, 129-134.
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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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