Archive ouverte UNIGE | last documentshttps://archive-ouverte.unige.ch/Latest objects deposited in the Archive ouverte UNIGEengDualities for infinite-dimensional projective geometrieshttps://archive-ouverte.unige.ch/unige:12653https://archive-ouverte.unige.ch/unige:12653abstract not availableFri, 26 Nov 2010 12:56:58 +0100On quasiconvex subgroups of word hyperbolic groupshttps://archive-ouverte.unige.ch/unige:12446https://archive-ouverte.unige.ch/unige:12446We prove that a quasiconvex subgroup H of in¢nite index of a torsion free word hyperbolic group can be embedded in a larger quasiconvex subgroup which is the free product of H and an in¢nite cyclic group. Some properties of quasiconvex subgroups ofword hyperbolic group are also discussed.Mon, 15 Nov 2010 12:42:32 +0100Dynamical 2-complexeshttps://archive-ouverte.unige.ch/unige:12442https://archive-ouverte.unige.ch/unige:12442abstract not availableMon, 15 Nov 2010 11:36:29 +0100Uniform Growth in Groups of Exponential Growthhttps://archive-ouverte.unige.ch/unige:12370https://archive-ouverte.unige.ch/unige:12370This is an exposition of examples and classes of finitely-generated groups which have uniform exponential growth. The main examples are non-Abelian free groups, semi-direct products of free Abelian groups with automorphisms having an eigenvalue of modulus distinct from 1, and Golod–Shafarevich infinite finitely-generated p-groups. The classes include groups which virtually have non-Abelian free quotients, nonelementary hyperbolic groups, appropriate free products with amalgamation, HNN-extensions and one-relator groups, as well as soluble groups of exponential growth. Several open problems are formulated.Mon, 08 Nov 2010 16:49:21 +0100Anti-tori in square complex groupshttps://archive-ouverte.unige.ch/unige:12148https://archive-ouverte.unige.ch/unige:12148An anti-torus is a subgroup $<a,b>$ in the fundamental group of a compact non-positively curved space $X$, acting in a specific way on the universal covering space $ ilde{X}$ such that $a$ and $b$ do not have any commuting non-trivial powers. We construct and investigate anti-tori in a class of commutative transitive fundamental groups of finite square complexes, in particular for the groups $Gamma_{p,l}$ originally studied by Mozes [15]. It turns out that anti-tori in $Gamma_{p,l}$ directly correspond to non-commuting pairs of Hamilton quaternions. Moreover, free anti-tori in $Gamma_{p,l}$ are related to free groups generated by two integer quaternions, and also to free subgroups of $mathrm{SO}_3(mathbb{Q})$. As an application, we prove that the multiplicative group generated by the two quaternions $1+2i$ and $1+4k$ is not free.Tue, 19 Oct 2010 12:56:05 +0200Sur la systole de la sphère au voisinage de la métrique standardhttps://archive-ouverte.unige.ch/unige:12125https://archive-ouverte.unige.ch/unige:12125We study the systolic area (defined as the ratio of the area over the square of the systole) of the 2-sphere endowed with a smooth Riemannian metric as a function of this metric. This function, bounded from below by a positive constant over the space of metrics, admits the standard metric g0 as a critical point, although it does not achieve the conjectured global minimum: we show that for each tangent direction to the space of metrics at g0, there exists a variation by metrics corresponding to this direction along which the systolic area can only increase.Mon, 18 Oct 2010 10:31:37 +0200Asymptotically Maximal Families of Hypersurfaces in Toric Varietieshttps://archive-ouverte.unige.ch/unige:12124https://archive-ouverte.unige.ch/unige:12124abstract not availableMon, 18 Oct 2010 09:31:58 +0200The true prosoluble completion of a group: Examples and open problemshttps://archive-ouverte.unige.ch/unige:9788https://archive-ouverte.unige.ch/unige:9788abstract not availableThu, 29 Jul 2010 14:38:13 +0200Some remarks on generalized roundnesshttps://archive-ouverte.unige.ch/unige:9752https://archive-ouverte.unige.ch/unige:9752By using the links between generalized roundness, negative type inequalities and equivariant Hilbert space compressions, we obtain that the generalized roundness of the usual Cayley graph of finitely generated free groups and free abelian groups of rank ≥2 equals 1. This answers a question of J-F. Lafont and S. Prassidis.Tue, 27 Jul 2010 14:49:47 +0200Collars and partitions of hyperbolic cone-surfaceshttps://archive-ouverte.unige.ch/unige:9706https://archive-ouverte.unige.ch/unige:9706For compact Riemann surfaces, the collar theorem and Bers' partition theorem are major tools for working with simple closed geodesics. The main goal of this article is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic two-dimensional orbifolds are a particular case of such surfaces. We consider all cone angles to be strictly less than π to be able to consider partitions.Mon, 26 Jul 2010 10:54:34 +0200On birational transformations of pairs in the complex planehttps://archive-ouverte.unige.ch/unige:6707https://archive-ouverte.unige.ch/unige:6707This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject.Fri, 28 May 2010 10:24:32 +0200