Groups, Geometry, and Dynamics
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Published online: 2016-06-09
Rigidity of extremal quasiregularly elliptic manifoldsRami Luisto and Pekka Pankka (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