Symplectically replacing plumbings with Euler characteristic 2 4-manifolds

Abstract

We introduce new symplectic cut-and-paste operations that generalize the rational blowdown. In particular, we will define $k$-replaceable plumbings to be those that, heuristically, can be symplectically replaced by Euler characteristic $k$ 4-manifolds. We will then classify 2-replaceable linear plumbings, construct 2-replaceable plumbing trees, and use one such tree to construct a symplectic exotic $\mathbb{C}{P}^2\#6\overline{\mathbb{C}{P}^2}$.

arXiv commentfinal version, minor typos fixed

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