Given a class of compact spaces, we ask which groups can be maximal parabolic subgroups of a relatively hyperbolic group whose boundary is in the class. We investigate the class of 1-dimensional connected boundaries. We get that any non-torsion infinite f.g. group is a maximal parabolic subgroup of some relatively hyperbolic group with connected one-dimensional boundary without global cut point...

We show that there does not exist a Kobayashi hyperbolic complex manifold of dimension n 6= 3, whose group of holomorphic automorphisms has dimension n2 + 1 and that, if a 3-dimensional connected hyperbolic complex manifold has automorphism group of dimension 10, then it is holomorphically equivalent to the Siegel space. These results complement earlier theorems of the authors on the possible d...

Abstract. In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form H/Γ where Γ is a torsion-free subgroup of minimal index of the congruence two subgroup Γ 2 of the group Γ of positive units of the Lorentzian quadratic form x 1 + · · ·+ x 5 − x 6 . We also show that Γ 2 is a reflection group with respect to a 5-dimensional right-angled convex po...

We define the notion of a “peripheral splitting” of a group. This is essentially a representation of the group as the fundamental group of a bipartite graph of groups, where all the vertex groups of one colour are held fixed—the “peripheral subgroups”. We develop the theory of such splittings and prove an accessibility result. The theory mainly applies to relatively hyperbolic groups with conne...

We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. Corollary: the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group. Mathematics Subject Classification (2000): 20E42, 54F35, 20F67

The isometry group of a compact n-dimensional hyperbolic man-ifold is known to be finite. We show that for every n ≥ 2, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n = 2 and n = 3 have been proven by Greenberg [G] and Ko-jima [K], respectively. Our proof is non constructive: it uses counting results from subgroup growth theory to sh...

Let D be the incidence graph of the projective plane over F3. The Artin group of the graph D maps onto the bimonster and a complex hyperbolic reflection group Γ acting on 13 dimensional complex hyperbolic space Y . The generators of the Artin group are mapped to elements of order 2 (resp. 3) in the bimonster (resp. Γ). Let Y ◦ ⊆ Y be the complement of the union of the fixed points of reflection...

The cephalic and pectoral girdle structures of the erethistid Erethistes pusillus (Erethistinae) are described and compared with those of another species of the subfamily Erethistinae, namely Hara filamentosa, and of the single species of the subfamily Continae, Conta conta, as well as of several other catfishes, as the foundation for a discussion on the synapomorphies and phylogenetic position...

We show that if G is a fundamental group of a finite k-acylindrical graph of groups where every vertex group is word-hyperbolic and where every edge-monomorphism is a quasi-isometric embedding, then all the vertex groups are quasiconvex in G (the group G is word-hyperbolic by the Combination Theorem of M.Bestvina and M.Feighn). This allows one, in particular, to approximate the word metric on G...

If M is a connected n-dimensional Kobayashi-hyperbolic complex manifold, then the group Aut(M) of holomorphic automorphisms of M is a (real) Lie group in the compact-open topology, of dimension d(M) not exceeding n + 2n, with the maximal value occurring only for manifolds holomorphically equivalent to the unit ball B ⊂ C [Ko1], [Ka]. We are interested in describing hyperbolic manifolds with low...