Homological dimension and critical exponent of Kleinian groups

Details Homological dimension and critical exponent of Kleinian groups Homological dimension and critical exponent of Kleinian groups

2007-01-28

arxiv.org/abs/math/0701797v1

Mathematics

Group Theory

38 pages

Scientific paper

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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