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) University of Helsinki, Finland
(2) University of 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