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- W2019050980 abstract "Abstract An extension of a result of Sela shows that if Γ is a torsion-free word hyperbolic group, then the only homomorphisms Γ→Γ with finite-index image are the automorphisms. It follows from this result and properties of quasiregular mappings, that if M is a closed Riemannian n -manifold with negative sectional curvature ( $nneq 4$ ), then every quasiregular mapping f : M → M is a homeomorphism. In the constant-curvature case the dimension restriction is not necessary and Mostow rigidity implies that f is homotopic to an isometry. This is to be contrasted with the fact that every such manifold admits a non-homeomorphic light open self-mapping. We present similar results for more general quotients of hyperbolic space and quasiregular mappings between them. For instance, we establish that besides covering projections there are no π 1 -injective proper quasiregular mappings f : M → N between hyperbolic 3-manifolds M and N with non-elementary fundamental group." @default.
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- W2019050980 date "2007-11-01" @default.
- W2019050980 modified "2023-10-04" @default.
- W2019050980 title "Quasiregular self-mappings of manifolds and word hyperbolic groups" @default.
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- W2019050980 doi "https://doi.org/10.1112/s0010437x07003028" @default.
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