Some lifting and approximation properties for maps in $W^{1,2}({\mathbb{B}}^3;{\mathbb{S}}^2)$

André Guerra, Xavier Lamy, Konstantinos Zemas

Smooth maps $u:{\mathbb{B}}^3\to {\mathbb{S}}^2$ can be lifted to $\hat{u}:{\mathbb{B}}^3\to {\mathbb{S}}^3$ using the Hopf fibration $h:{\mathbb{S}}^3\to {\mathbb{S}}^2$ via the factori…