Objetivo Results involving all finitely generated groups are often of very little interest, and therefore combinatorial group theory concentrates on particular classes of groups. Hyperbolic groups form one of the classes that offer an extremely satisfactory compromise between interest and generality, as one can prove very precise structural results for such groups. In our project we propose to work on relatively hyperbolic groups, which are a generalisation of hyperbolic groups, and on some other questions involving the techniques and methods of the related theories. There are already several characterisations of relatively hyperbolic groups from different points of view, like dynamical or topological. One of the problems that we propose here is to give a cohomological characterisation of relatively hyperbolic groups, namely to study the relative bounded cohomology and to understand the connection between bounded cohomology and standard cohomology. Another problem we would like to work on involves relative metabolicity. It has been proved that relative metabolicity implies weak relative hyperbolicity. It would be an attractive result to strengthen this result, and to show that relative metabolicity actually implies relative hyperbolicity in the strong sense. The third problem is a natural continuation of an earlier work, and aims to find out which classes of finitely generated groups satisfy the "property of special symbol". This property was introduced in order to encode the action of relatively hyperbolic groups on their boundaries by means of symbolic dynamics. Finally, I would like to weaken the hypotheses of a recent result on configuration spaces and cocompact properly discontinuous group actions. This question and the methods to approach it involve the techniques that were used to give a dynamical characterisation of relatively hyperbolic groups. If the hypotheses are formulated in their greatest generality, this will be an attra Ámbito científico natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicspure mathematicsgeometry Palabras clave Geometric Group Theory Programa(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Tema(s) MOBILITY-2.1 - Marie Curie Intra-European Fellowships (EIF) Convocatoria de propuestas FP6-2002-MOBILITY-5 Consulte otros proyectos de esta convocatoria Régimen de financiación EIF - Marie Curie actions-Intra-European Fellowships Coordinador CENTRE DE RECERCA MATEMATICA Aportación de la UE Sin datos Dirección BELLATERRA España Ver en el mapa Enlaces Sitio web Opens in new window Coste total Sin datos