Andreotti–Frankel theorem

In mathematics, the Andreotti–Frankel theorem, introduced by Andreotti and Frankel (1959), states that if ${\displaystyle V}$ is a smooth affine variety of complex dimension ${\displaystyle n}$ or, more generally, if ${\displaystyle V}$ is any Stein manifold of dimension ${\displaystyle n}$, then in fact ${\displaystyle V}$ is homotopy equivalent to a CW complex of real dimension at most n. In other words ${\displaystyle V}$ has only half as much topology.

...
Wikipedia