The Euler characteristic and inequalities for Kleinian groups

Abikoff, William

doi:10.1090/S0002-9939-1986-0845971-7

The Euler characteristic and inequalities for Kleinian groups
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by William Abikoff

Proc. Amer. Math. Soc. 97 (1986), 593-601

DOI: https://doi.org/10.1090/S0002-9939-1986-0845971-7

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Abstract:

A class of torsion-free finitely generated Kleinian groups is defined. For groups $G$ in this class, sharp versions—with error terms—of standard inequalities are given. Also, sharp estimates are given for the number of cusps and the sum of the ranks of maximal nonconjugate cyclic parabolic subgroups.

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