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 Mar 11 comment Computations in group cohomology Thank you for this precise answer. I will try to do this and post again if there is a problem. Mar 11 accepted Computations in group cohomology Mar 10 asked Computations in group cohomology Mar 9 comment Isotropic subspaces in cohomology This is a nice example and seems to show that in high dimensions such examples are not at all pathological. Do you think than we can obtain in this way a result like : "a generic finitely presentable group (with sufficiently generators and relations) does not verify $g_\mathcal{R} = g_\mathcal{C}$" ? Mar 9 accepted Isotropic subspaces in cohomology Mar 8 comment Isotropic subspaces in cohomology You are right, in full generality this is a question of linear algebra but maybe one can say something when the question is restricted to some class of manifolds. For instance this seems to be true for Kähler manifolds and I want to see if this has something to do with Hodge decomposition. Mar 8 asked Isotropic subspaces in cohomology Jan 26 awarded Scholar Jan 26 accepted Groups with large negative deficiency Jan 26 accepted Cohomological dimension of a group, fibration and local coefficients Jan 26 comment Cohomological dimension of a group, fibration and local coefficients I'm sorry M. Kent, I made a mistake in writing : What I want is to prove that there is no Kähler group of cohomological dimension three. Jan 26 asked Groups with large negative deficiency Jan 26 comment Cohomological dimension of a group, fibration and local coefficients I don't think so because in a way I try to prove something stronger. In fact we can adapt the proof in this article to show that if the cohomology of G satisfies 3-dimensional Poincaré duality, then we have a contradiction. What I want to prove is that there is no Kähler group of cohomological dimension one, without assumptions of Poincaré duality. Jan 26 comment Cohomological dimension of a group, fibration and local coefficients Yes and in fact this is my original problem, where G is a Kähler group and the epimorphism is induced by the Albanese map (G has 1-dimensional Albanese image). Jan 26 awarded Student Jan 26 asked Cohomological dimension of a group, fibration and local coefficients