Homological dimension and critical exponent of Kleinian groups

2007/01/28 by Kapovich, Michael · 2 citations
#20F67 #30F40 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0701797

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.

Cited by

• Scalar Curvature in Dimension 4
• Finite Index Rigidity of Relatively Hyperbolic Groups

Related

• Hausdorff dimension and Kleinian groups
• Critical exponents and dimension for generalised limit sets
• The Poincaré exponent and the dimensions of Kleinian limit sets
• The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group
• Hausdorff dimension of non-conical limit sets