Extended explanation of Orevkov's paper on proper holomorphic embeddings of complements of Cantor sets in ${\mathbb{C}}^2$ and a discussion of their measure

Abstract

We clarify the details of a cryptical paper by Orevkov in which a construction of a proper holomorphic embedding $\gamma :{\mathbb{P}}^1\setminus C\hookrightarrow {\mathbb{C}}^2$ is performed; in particular, it is proved that such a construction can be done to get the Cantor set $C$ to have zero Hausdorff dimension.