3 problems

Let $X$ be a topologically contractible smooth complex affine variety, and let $x\in X({\mathbb C})$ be a chosen base-point. Write $\Sigma^n_{{\mathbb P}^1}(X,x)$ for the $n$-fold…

Let $X$ be a smooth topologically contractible surface. Surface contractibility conjecture. The variety $X$ is ${\mathbb A}^1$-contractible if and only if it is isomorphic to…

Let $X$ be a topologically contractible smooth complex variety with a chosen base-point $x\in X({\mathbb C})$. Write $\Sigma^n_{{\mathbb P}^1}(X,x)$ for the $n$-fold…