Subgroups of the modular group defined by a single linear congruence
Sur certains groupes fuchsiens et sur une extension de la théorie des formes quadratiques
Sur la détermination des fonctions qui admettent les substitutions d'un groupe donné, et seulement ces substitutions-là
Sur la fonction orbitale des groupes discrets en courbure négative
Nous précisons le comportement exponentiel de la fonction orbitale d'un quelconque groupe discret d'isométries en courbure négative.
Sur la théorie des invariants des groupes classiques
On donne une forme géométrique à la théorie classique des invariants pour le groupe spécial linéaire, le groupe orthogonal et le groupe symplectique. On démontre aussi un critère de normalité pour les variétés algébriques affines où opère un groupe algébrique réductif connexe.
Sur les notions de fonction complète et de fonction périodique
Sur les substitutions à une variable et les fonctions qu'elles laissent invariables
Sur les valeurs propres de la transformation de Coxeter.
Surfaces réglées non compactes et groupes discrets.
Symmetries of planar growth functions.
Symmetry groups and fundamental tilings for the compact surface of genus . II: The normalizer diagram with classification.
Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere
We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system....
Systoles of arithmetic surfaces and the Markoff spectrum.
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