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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 |