Abstract
The growth of the fundamental group of a Riemannian manifold can be used to prove the nonexistence of quasiregular mappings from the Euclidean space to the manifold. Some constructive methods provide existence results. This paper is a preliminary report on a study of these problems.
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Bibliography
Milnor, J.: ‘A note on curvature and fundamental group’, J. Diff. Geom. 2, (1968), 1–7.
Milnor, J.: ‘Growth of finitely generated solvable groups’, ibid. 2, (1968), 447–49.
Gromov, M.: ‘Groups of polynomial growth and expanding maps’, Publ. Math. I.H.E.S. 53 (1981), 53–73.
Gromov, M.: ‘Hyperbolic manifolds, groups and actions’, Ann. Math. Studies 97 Conf. Stony Brook 1978, 183–213.
Pansu, P.: ‘An isoperimetric inequality on the Heisenberg group’, CR. Acad. So. Paris 295 (1982), 127–130.
Wolf, J.: ‘Growth of finitely generated solvable groups and curvature of Riemannian manifolds’, J. Diff. Geom. 2 (1968), 421–446.
Bass, H.: ‘The degree of polynomial growth of finitely generated nilpotent groups’, Proc. Lond. M.S. (3) 25 (1972), 602–614.
Grigorchuk, R.I.: ‘Degrees of growth of finitely generated groups and the theory of invariant means’, Math. USSR Iz. 25 (1985), 259–99.
Rosenblatt, J.: ‘Invariant measures and growth conditions’, Trans. Amer. M.S. 193 (1974), 33–53.
Evans, B. and Moser, L.: ‘Solvable fundamental groups of compact 3-manifolds’, Trans. Amer. M.S. 168 (1972), 189–210.
Jormakka, J.: ‘Existence of quasiregular mappings from ℝ3 to closed orientable 3-manifolds’, to appear.
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© 1989 Kluwer Academic Publishers
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Jormakka, J. (1989). Quasiregular Mappings from Rn to Closed Orientable n-Manifolds. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2643-1_3
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DOI: https://doi.org/10.1007/978-94-009-2643-1_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7693-7
Online ISBN: 978-94-009-2643-1
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