We construct an example of a large exotic $\mathbb{R}^4$ which is the complement of a topologically embedded sphere $S^2$ in $\mathbb{C}P^2$. We can represent a certain homological $2$-class of the manifold $\mathbb{C}P^2 \# 9 \overline{\mathbb{C} P^2}$ by a topologically embedded $2$-sphere $S$ using Casson handles and Freedman's theorem \cite{freedman_paper}. Every Casson handle embeds smoothly in a $2$-handle, therefore there exists a smooth embedding $\iota: U \rightarrow \mathbb{C}P^2$ of an open neighborhood $U$ of the sphere $S$ in $\mathbb{C}P^2$. The complement $R = \mathbb{C} P^2 - \iota(S)$ is by the work of Freedman homeomorphic to $\mathbb{R}^4$. However, it follows by Donaldson's theorem \cite{donaldson} there does not exist a smooth embedding of $R$ in $\mathbb{R}^4$, so $R$ is a large exotic $\mathbb{R}^4$.
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