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

Potyagaĭlo, L.

doi:10.1090/S0002-9947-1994-1250823-6

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