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Transactions of the American Mathematical Society

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Finitely generated Kleinian groups in $ 3$-space and $ 3$-manifolds of infinite homotopy type


Author: L. Potyagaĭlo
Journal: Trans. Amer. Math. Soc. 344 (1994), 57-77
MSC: Primary 57M50; Secondary 20H10, 30F40, 57N10, 57S30
DOI: https://doi.org/10.1090/S0002-9947-1994-1250823-6
MathSciNet review: 1250823
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Abstract: We prove the existence of a finitely generated Kleinian group $ N \subset S{O_ + }(1,4)$ acting freely on an invariant component $ \Omega \subset {S^3}$ without parabolic elements such that the fundamental group $ {\pi _1}(\Omega /N)$ is not finitely generated.

Moreover, N is a finite index subgroup of a Kleinian group $ {N_0}$ which has infinitely many conjugacy classes of elliptic elements.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1994-1250823-6
Keywords: Kleinian groups, conformal group of euclidean space, uniformization of 3-manifolds, surface bundle over the circle
Article copyright: © Copyright 1994 American Mathematical Society

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