# Groups, Geometry, and Dynamics

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**Volume 10, Issue 2, 2016, pp. 723–732**

**DOI: 10.4171/GGD/362**

Rigidity of extremal quasiregularly elliptic manifolds

Rami Luisto^{[1]}and Pekka Pankka

^{[2]}(1) Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland

(2) Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, 40014, Jyväskylä, Finland

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.

*Keywords: *Quasiregular mappings, quasiregular ellipticity, Loewner spaces, crystallographic groups

Luisto Rami, Pankka Pekka: Rigidity of extremal quasiregularly elliptic manifolds. *Groups Geom. Dyn.* 10 (2016), 723-732. doi: 10.4171/GGD/362