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Homological dimension and critical exponent of Kleinian groups

Michael Kapovich
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Abstract

We prove that the relative homological dimension of a Kleinian group G does not exceed 1 + the critical exponent of G. As an application of this result we show that for a geometrically finite Kleinian group G, if the topological dimension of the limit set of G equals its Hausdorff dimension, then the limit set is a round sphere.

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Michael Kapovich. 2007-01-28. Homological dimension and critical exponent of Kleinian groups. https://arxiv.org/abs/math/0701797

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