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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Finitely generated Kleinian groups in $3$-space and $3$-manifolds of infinite homotopy type
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by L. Potyagaĭlo PDF
Trans. Amer. Math. Soc. 344 (1994), 57-77 Request permission

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
  • © Copyright 1994 American Mathematical Society
  • 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