Talk:Čech cohomology

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[edit] Less technical intro?

It's got very technical, hasn't it? The original Cech definition wouldn't have been for a general presheaf, but something more like a constant sheaf. Could we have an introductory section saying something about cochains with integer values?

Charles Matthews 11:08, 17 December 2005 (UTC)

I agree with you. I think we should have a more straight forward example. I will try to write something down if there is a good example.

Hwasungmars (talk) 12:01, 29 December 2007 (UTC)

[edit] A priori or direct limit?

Is the Čech cohomlogy, \check{H}^*(X;A) a cohomology a priori, or is it just the direct limit of a set of cohomologies, with the direct limit being isomorphic to specific Čech cohomlogies, H^*(\bold{U},\mathbb{R}), with respect to good open covers, as a consequence of a Theorem? Figaro 14:57, 8 February 2006 (UTC)

[edit] Explicit isomorphism?

I'd like to see the isomorphisms worked out in detail, e.g. the iso to de Rham. (never mind, the article on de Rham cohomology provides a breif review of this isomorphism). Also, some examples on how to compute these things, e.g. if the space X is not a differentiable manifold, but something else (I'm interested in the topology of cylinder sets). linas 01:35, 14 September 2006 (UTC)

[edit] de Rham isomorphic?

I was wondering about the de Rham isomorphism. In Bott&Tu there is a proof of this for finite good covers. Does this isomorphism still exist otherwise? I think this ought to be clarified.

The definition itself seems very messy too. —Preceding unsigned comment added by 130.88.0.79 (talk) 00:21, 6 May 2008 (UTC)