# Rigidity of extremal quasiregularly elliptic manifolds

### Rami Luisto

University of Helsinki, Finland### Pekka Pankka

University of Jyväskylä, Finland

## 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 $\Z^n$ and torsion free.

## Cite this article

Rami Luisto, Pekka Pankka, Rigidity of extremal quasiregularly elliptic manifolds. Groups Geom. Dyn. 10 (2016), no. 2, pp. 723–732

DOI 10.4171/GGD/362