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On the absence of Sullivan’s cusp finiteness theorem in higher dimensions. (English) Zbl 0840.57023
Bokut’, L. A. (ed.) et al., Third Siberian school on algebra and analysis. Proceedings of the third Siberian school, Irkutsk State University, Irkutsk, Russia, August 30-September 4, 1989. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 163, 77-89 (1995).
Summary: We prove the existence of a discontinuous finitely generated free conformal group \(K_3\) acting on \(\mathbb{R}^3\) such that the number of rank 1 cusps of \(K_3\) is infinite. Small deformations of \(K_3\) provide a finitely generated Kleinian group with infinitely many conjugacy classes of finite order elements.
For the entire collection see [Zbl 0816.00016].

MSC:
57S30 Discontinuous groups of transformations
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
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