arXiv subjects
Publications and source records attributed to Jean-Philippe Preaux.
We give explicit formulas as well as a quadratic time algorithm to solve (so called) generalized Vandermonde's systems of p linear equations and n variables. It allows in particular to find all (so called Lagrange's) interpolation polynoms with degree n-1 taking given values in p distinct points.
We characterize the group property of being with infinite conjugacy classes (or icc, i.e. in which all conjugacy classes beside 1 are infinite) for split extensions of groups.
We characterize the group property of being with infinite conjugacy classes (or icc, in which all conjugacy classes beside 1 are infinite) for extensions of some specific groups ; namely extensions of abelian, centerless, icc, or word hyperbolic groups.
We characterize the group property of being with infinite conjugacy classes (or icc, i.e. \not= 1 and of which all conjugacy classes except 1 are infinite) for finite extensions of group.
Nous rappelons l'historique de la demonstration de la conjecture des fibres de Seifert, ainsi que ses motivations et ses diverses generalisations. ----- We recall the history of the proof of the Seibert fiber space conjecture, as well as its motivations and diverse generalizations.
This work is concerned with the stable norm in word hyperbolic groups as defined by Gromov. We give a short elementary proof of one of its basic property, that is existence of a computable uniform non null lower bound for stable norm in a word hyperbolic group.
Nous explicitons les centralisateurs dans un sous-groupe discret cocompact d'isometrie du plan euclidien ----- We make explicit the centralizers of a discrete cocompact subgroup of isometries of the Euclidean plane.
We give solutions to several decision problems in word hyperbolic groups
We characterise the group property of being with infinite conjugacy classes for wreath products of groups
We have proved in [Topology, 45 1 (2006)] that fundamental groups of oriented geometrizable 3-manifolds have a solvable conjugacy problem. We now consider the case of groups of non-oriented geometrizable 3-manifolds in order to conclude that fundamental groups of geometrizable 3-manifolds all have a solvable conjugacy problem.
We consider the group property of being icc. We give several examples of icc groups and study its stability under usual algebraic constructions.
We give characterizations of the center, of conjugated and of commuting elements in a fundamental group of a graph of group. We deduce various results : on the one hand we give a sufficient condition for the center, the centralizers, and the root structures in such a group to be in some sense trivial, and on the other hand we prove that for any group G, the conjugacy problem reduces to the same problem in a double of G along any finite family of subgroups.
We provide a geometric characterization of manifolds of dimension 3 with fundamental groups of which all conjugacy classes except 1 are infinite, namely of which the von Neumann algebras are factors of type $II_1$: they are essentially the 3-manifolds with infinite fundamental groups on which there does not exist any Seifert fibration. Otherwise said and more precisely, let $M$ be a compact connected 3-manifold and let $Γ$ be its fundamental group, supposed to be infinite and with at least one finite conjugacy class besides 1. If $M$ is orientable, then $Γ$ is the fundamental group of a Seifert manifold; if $M$ is not orientable, then $Γ$ is the fundamental group of a Seifert manifold modulo $\Bbb P$ in the sense of Heil and Whitten \cite{HeWh--94}. We make heavy use of results on 3-manifolds, as well classical results (as can be found in the books of Hempel, Jaco, and Shalen), as more recent ones (solution of the Seifert fibred space conjecture).