Après-midi de théorie des groupes

Tuesday, 22 January14.00-14.45 Bertrand Rémy (Ecole Polytechnique)15.00-15.45 Tom Hutchcroft (Cambridge)15.45-16.15 coffee break16.15-17.00 Pavel Zalesski (University of Brasilia)Bertrand Remy, Quasi-isometric invariance of continuous group Lp-cohomology, and first applications to vanishings (joint with Marc Bourdon)We show that the continuous L^p-cohomology of locally compact second countable groups is a quasi-isometric invariant. As an application, we prove partial results supporting a positive answer to a question asked by M. Gromov, suggesting a classical behaviour of continuous L^p-cohomology of simple real Lie groups. In addition to quasi-isometric invariance, the ingredients are a spectral sequence argument and Pansu?RTMs vanishing results for real hyperbolic spaces. In the best adapted cases of simple Lie groups, we obtain nearly half of the relevant vanishings. Tom Hutchcroft, Kazhdan groups have cost 1I will sketch a proof that Kazhdan groups have cost 1, answering a question of Gaboriau. No knowledge of Kazhdan groups or of cost will be assumed. Joint work with Gabor Pete.Pavel Zalesski, The profinite completion of 3-manifold groups.Abstract. We shall present structural results of the profinite completion widehat G of a 3-manifold group G and its interrelation with the structure of G. We shall address the question to what extent the profinite completion of the fundamental group $pi_1M of a 3-manifold determines the manifold M and discuss residual properties of pi_1 M.