Small exotic rational surfaces without 1- and 3-handles

Yasui, Kouichi

doi:10.1090/S0002-9947-2010-05205-5

Small exotic rational surfaces without 1- and 3-handles
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Trans. Amer. Math. Soc. 362 (2010), 5893-5907 Request permission

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.

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