So

I've been asking around a little, and nobody seems to be able to tell whether or not Russell's hypersurface is analytically $\mathbb C^3$. Adrien Dubouloz shows in this article that the Makar-Limanov invariant of its product with $\mathbb C$ is where you should put all your welcome upvotestrivial. Thanks!Maybe that helps.

So, this is where you should put all your welcome upvotes. Thanks!