Braids: generalizations, presentations and algorithmic properties.
Canonical representatives and equations in hyperbolic groups.
Caractérisation algébrique des groupes de type fini ayant un problème de mots résoluble (théorème de Boone-Higman, travaux de B. H. Neumann et MacIntyre)
Centraliser dimension and universal classes of groups.
Combing Euclidean buildings.
Commutativity in groups presented by finite Church-Rosser Thue systems
Complete presentations of Coxeter groups.
Complexity of some natural problems in automatic structures.
Computation of centralizers in Braid groups and Garside groups.
We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conjugacy problem given by the authors in [9], are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2]. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers.
Cônes asymptotiques et invariants de quasi-isométrie pour les espaces métriques hyperboliques
On utilise l'équivalence due à M. Gromov entre l'hyperbolicité d'un espace métrique géodésique et le fait que ses cônes asymptotiques sont des arbres réels. Ce résultat permet tout d'abord de donner une nouvelle preuve du fait que l'inégalité isopérimétrique sous-quadratique implique l'hyperbolicité. Les avantages de cette preuve sont qu'elle est très courte et qu'elle utilise une seule propriété de la fonction aire de remplissage des courbes fermées, l'inégalité du quadrilatère....
Cubical sets and their site.
(Cyclic) subgroup separability of HNN and split extensions
Derivation-Bounded Groups.
Diophantine geometry over groups I : Makanin-Razborov diagrams
This paper is the first in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the first paper we present the (canonical) Makanin-Razborov diagram that encodes the set of solutions of a system of equations. We continue by studying parametric families of sets of solutions, and associate with such a family a canonical graded Makanin-Razborov diagram, that encodes the collection...
Eine Bemerkung zu den Nielsen-Transformationen.
Eine rekursiv präsentierte Gruppe mit unentscheidbarem Wortlaut.
Equivalence élémentaire entre groupes finis-par-abéliens de type fini.
Every braid admits a short sigma-definite expression
A result by Dehornoy (1992) says that every nontrivial braid admits a -definite expression, defined as a braid word in which the generator with maximal index appears with exponents that are all positive, or all negative. This is the ground result for ordering braids. In this paper, we enhance this result and prove that every braid admits a -definite word expression that, in addition, is quasi-geodesic. This establishes a longstanding conjecture. Our proof uses the dual braid monoid and a new...
Existentially closed -groups
Existentially Closed Locally Finite Central Extensions: Multipliers and Local Systems.