  We consider quasiconformal deformations of $\mathbb{C}\setminus\mathbb{Z}$.
We give some criteria for infinitely often punctured planes to be
quasiconformally equivalent to $\mathbb{C}\setminus\mathbb{Z}$. In particular,
we characterize the closed subsets of $\mathbb{R}$ whose compliments are
quasiconformally equivalent to $\mathbb{C}\setminus\mathbb{Z}$.

Differential Geometry