The bounded model for hyperbolic 3-space and a quaternionic uniformization theorem.
The box-counting dimension for geometrically finite Kleinian groups
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 Cayley graphs of and the limits of vertex-primitive graphs of -type.
The central heights of stability groups of series in vector spaces
We compute the central heights of the full stability groups of ascending series and of descending series of subspaces in vector spaces over fields and division rings. The aim is to develop at least partial right analogues of results on left Engel elements and related nilpotent radicals in such proved recently by Casolo & Puglisi, by Traustason and by the current author. Perhaps surprisingly, while there is an absolute bound on these central heights for descending series, for ascending series...
The characters of the hecatonicosahedroidal group.
The classification of space groups.
The congruence subgroup problem for algebraic groups
The connected components on the projective line over a ring.
The connections between continued fraction representations of units and certain Hecke groups.
The determination of parabolic points in modular and extended modular groups by continued fractions.
The Farey graph.
The finite subgroups of maximal arithmetic kleinian groups
Given a maximal arithmetic Kleinian group , we compute its finite subgroups in terms of the arithmetic data associated to by Borel. This has applications to the study of arithmetic hyperbolic 3-manifolds.
The full automorphism group of the Kulkarni surface.
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.
The full automorphism groups of hyperelliptic Riemann surfaces.
The fundamental theorem for the projective line over commutative rings. (Short Communication).
The fundamental theorem for the projective line over commutative rings.
The geometry and spectrum of the one holed torus.
The integral homology of SL2 and PSL2 of euclidean imaginary quadratic integers.
The length of a unitary transformation.
The length of a unitary transformation for characteristic 2.