Small exotic rational surfaces without 1- and 3-handles
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Abstract:
We give new rational blowdown constructions of exotic $\mathbf {CP}^2\# n\overline {\mathbf {C}\mathbf {P}^2}$ $(5\leq n\leq 9)$ 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 $\mathbf {CP}^2\# n\overline {\mathbf {C}\mathbf {P}^2}$ $(1\leq n\leq 4)$ is also proposed.References
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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
- 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.
- © Copyright 2010 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 362 (2010), 5893-5907
- MSC (2010): Primary 57R55; Secondary 57R65, 57N13
- DOI: https://doi.org/10.1090/S0002-9947-2010-05205-5
- MathSciNet review: 2661501