%0 Journal Article %T Quasiregular ellipticity of open and generalized manifolds %A Pekka Pankka %A Kai Rajala %A Jang-Mei Wu %J Mathematics %D 2013 %I arXiv %X We study the existence of geometrically controlled branched covering maps from $\mathbb R^3$ to open $3$-manifolds or to decomposition spaces $\mathbb S^3/G$, and from $\mathbb S^3/G$ to $\mathbb S^3$. %U http://arxiv.org/abs/1310.8595v1