Abstract
Suppose that M is a closed, connected, and oriented Riemannian n-manifold, f: ℝn → M is a quasiregular map automorphic under a discrete group Γ of Euclidean isometries, and f has finite multiplicity in a fundamental cell of Γ. We show that if Γ has a sufficiently large translation subgroup ΓT, then dim Γ ∈ {0, n − 1, n}. If f is strongly automorphic and induces a non-injective Lattès-type uniformly quasiregular map, then the same assertion holds without the assumption on the size of ΓT. Moreover, an even stronger restriction holds in the Lattès case if M is not a rational cohomology sphere.
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This work was supported by the doctoral program DOMAST of the University of Helsinki and the Academy of Finland project #297258.
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Kangasniemi, I. Obstructions for automorphic quasiregular maps and Lattès-type uniformly quasiregular maps. JAMA 146, 401–439 (2022). https://doi.org/10.1007/s11854-021-0187-y
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DOI: https://doi.org/10.1007/s11854-021-0187-y