基于$\mathbb{CP}^{2}$中直线和二次曲面的小奇异4-流形
Small exotic 4-manifolds from lines and quadrics in $\mathbb{CP}^{2}$
摘要：
我们构造潜在的新的流形同胚，但不同胚$\mathbb{CP}^{2} \# 8 \overline{\mathbb{CP}^{2}}$和$\mathbb{CP}^{2} \# 9 \overline{\mathbb{CP}^{2}}$通过合理的吹除手术沿某些$4$ -valent铅垂图。这样，所有的图类从\cite{weighted}有一个代表，承认一个合理的排污导致一个奇异的流形。我们强调简单的建设归结为找到一个很好的配置复杂的线和二次曲面在$\mathbb{CP}^{2}$，并决定哪些路口炸毁。
英文摘要：
We construct potentially new manifolds homeomorphic but not diffeomorphic to $\mathbb{CP}^{2} \# 8 \overline{\mathbb{CP}^{2}}$ and $\mathbb{CP}^{2} \# 9 \overline{\mathbb{CP}^{2}}$ via rational blowdown surgery along certain $4$-valent plumbing graphs. This way all the graph classes from \cite{weighted} have a representative which admits a rational blowdown leading to an exotic manifold. We emphasize the simplicity of the constructions which boils down to finding a good configuration of complex lines and quadrics in $\mathbb{CP}^{2}$, and deciding which intersections to blow up.
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