Talk:Čech cohomology

From Wikipedia, the free encyclopedia

[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)

[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)

Retrieved from "http://en.wikipedia.org../../../%C4%8D/e/c/Talk%7E%C4%8Cech_cohomology_b719.html"