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 $\mathbb{C}P^2\#6\overline{\mathbb{C}P^2}$.

中文翻译：

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用欧拉特征 $2 \: 4$‑manifolds 辛替换管道

我们引入了新的辛剪切和粘贴操作来概括理性排污。特别地，我们将定义 $k$-replaceable 管道是那些启发式地可以被欧拉特征 $k$ 4-流形辛替换的管道。然后我们将对 2-replaceable 线性管道进行分类，构造 2-replaceable 管道树，并使用这样的一棵树来构造一个辛奇异的 $\mathbb{C}P^2\#6\overline{\mathbb{C}P^2 }$。