Rigidity of extremal quasiregularly elliptic manifolds

Abstract

We show that for a closed $n$-manifold $N$ admitting a quasiregular mapping from Euclidean $n$-space the following are equivalent: (1) order of growth of ${\pi }_1(N)$ is $n$, (2) $N$ is aspherical, and (3) ${\pi }_1(N)$ is virtually ${\mathbb{Z}}^n$ and torsion free.