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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Circle-sum and minimal genus surfaces in ruled 4-manifolds
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by Bang-He Li and Tian-Jun Li PDF
Proc. Amer. Math. Soc. 135 (2007), 3745-3753 Request permission

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.
References
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  • Bang-He Li and Tian-Jun Li, Symplectic genus, minimal genus and diffeomorphisms, Asian J. Math. 6 (2002), no. 1, 123–144. MR 1902650, DOI 10.4310/AJM.2002.v6.n1.a7
  • Bang-He Li and Tian-Jun Li, Minimal genus embeddings in $S^2$-bundles over surfaces, Math. Res. Lett. 4 (1997), no. 2-3, 379–394. MR 1453068, DOI 10.4310/MRL.1997.v4.n3.a7
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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
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 3745-3753
  • MSC (2000): Primary 57R40, 57R57; Secondary 57R17
  • DOI: https://doi.org/10.1090/S0002-9939-07-08954-X
  • MathSciNet review: 2336591