Exotic affine space

Short description: Real affine space of even dimension that is not isomorphic to a complex affine space

In algebraic geometry, an exotic affine space is a complex algebraic variety that is diffeomorphic to ${\mathbb{ℝ}}^{2n}$ for some n, but is not isomorphic as an algebraic variety to ${\mathbb{ℂ}}^n$. An example of an exotic ${\mathbb{ℂ}}^3$ is the Koras–Russell cubic threefold, which is the subset of ${\mathbb{ℂ}}^4$ defined by the polynomial equation

$\{(z_1,z_2,z_3,z_4)\in {\mathbb{ℂ}}^4|z_1+z_1^2{z}_2+z_3^3+z_4^2=0\}.$