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The box-counting dimension for geometrically finite Kleinian groups

B. Stratmann, Mariusz Urbański (1996)

Fundamenta Mathematicae

We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the 'global measure formula' for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we conclude that for a geometrically finite group these three different types of dimension coincide with the...

The finite subgroups of maximal arithmetic kleinian groups

Ted Chinburg, Eduardo Friedman (2000)

Annales de l'institut Fourier

Given a maximal arithmetic Kleinian group Γ ⊂ PGL ( 2 , ℂ ) , we compute its finite subgroups in terms of the arithmetic data associated to Γ by Borel. This has applications to the study of arithmetic hyperbolic 3-manifolds.

The full automorphism group of the Kulkarni surface.

Peter Turbek (1997)

Revista Matemática de la Universidad Complutense de Madrid

The full automorphism group of the Kulkarni surface is explicitly determined. It is employed to give three defining equations of the Kulkarni surface; each equation exhibits a symmetry of the surface as complex conjugation.

Theory of coverings in the study of Riemann surfaces

Ewa Tyszkowska (2012)

Colloquium Mathematicae

For a G-covering Y → Y/G = X induced by a properly discontinuous action of a group G on a topological space Y, there is a natural action of π(X,x) on the set F of points in Y with nontrivial stabilizers in G. We study the covering of X obtained from the universal covering of X and the left action of π(X,x) on F. We find a formula for the number of fixed points of an element g ∈ G which is a generalization of Macbeath's formula applied to an automorphism of a Riemann surface. We give a new method...

Traces, lengths, axes and commensurability

Alan W. Reid (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.

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