Groups, Geometry, and Dynamics
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Rigidity of extremal quasiregularly elliptic manifoldsRami Luisto and Pekka Pankka (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