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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Small exotic rational surfaces without 1- and 3-handles


Author: Kouichi Yasui
Journal: Trans. Amer. Math. Soc. 362 (2010), 5893-5907
MSC (2010): Primary 57R55; Secondary 57R65, 57N13
Published electronically: June 2, 2010
MathSciNet review: 2661501
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Abstract: We give new rational blowdown constructions of exotic $ \mathbf{CP}^2\char93 n\overline{\mathbf{C}\mathbf{P}^2}$ $ (5\leq n\leq 9)$ without using elliptic fibrations. We also show that our 4-manifolds admit handle decompositions without 1- and 3-handles, for $ 7\leq n\leq 9$. A strategy for rational blowdown constructions of exotic $ \mathbf{CP}^2\char93 n\overline{\mathbf{C}\mathbf{P}^2}$ $ (1\leq n\leq 4)$ is also proposed.


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Additional Information

Kouichi Yasui
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
Address at time of publication: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
Email: kyasui@cr.math.sci.osaka-u.ac.jp, kyasui@math.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05205-5
PII: S 0002-9947(2010)05205-5
Keywords: Handle decomposition, rational blowdown, $1$-handle, small exotic $4$-manifold.
Received by editor(s): August 6, 2008
Published electronically: June 2, 2010
Additional Notes: The author was partially supported by JSPS Research Fellowships for Young Scientists, and by GCOE, Kyoto University.
Article copyright: © Copyright 2010 American Mathematical Society