# Proper analytic embedding of $\overline{\Bbb C}$ minus a Cantor set into $\Bbb C^2$

I am a PhD student in several complex variables. I am reading this paper by Orevkov proving that there exists a proper analytic embedding of $$\overline{\Bbb C}$$ minus a Cantor set into $$\Bbb C^2$$.

I am really lost and I am writing here to ask some hint/tips on how to proceed reading it. It is not clear why $$K$$ is a Cantor set, since in order to find out (analytically) its elements one should find roots of $$n$$-degree polynomials (for all $$n\ge1$$, and no recursive formula seems to appear). Someone suggested me to argue geometrically, but it is very hard and, anyhow, it doesn't seem to help (for what I tried so far).

Also I cannot see how to prove points 2), 3) and 4) and how does are the exploited in the rest of this short but very dense paper.

Thanks. Of course I don't ask a clear proof of this, but just some guidelines I can follow to going out of this labyrinth.

• I have no access to the paper, but the formulation is ambiguous: does it mean $\mathbf{C}$ minus some Cantor subset, or minus every Cantor subset? while topologically these are all "the same", up to biholomorphy it's far from unique.
– YCor
Mar 18, 2020 at 14:17