Talk:Classifying space

Definition

Definition by homotopy groups: well, I don't think that's in good taste, and I see User:Waltpohl thinks it's suspect. So perhaps we should look to have the weak equivalence page written, which would allow one to explain why (and to what extent) anyone might come up with such a definition. Also someone to write the Eilenberg-Mac Lane space page, so we can start untangling this, without junking the intuitions right now.

Charles Matthews 11:48, 6 Sep 2004 (UTC)

Lost

I'm lost at the beginning: "It has the property that any G principal bundle over a paracompact manifold is isomorphic to a pullback of the principal bundle." A pull back induced by what map? The only map even hinted at is the quotient map, but it is not obvious how this map is related to the arbitrary paracompact manifold. Dewa (talk) 02:45, 12 April 2008 (UTC)[reply]

Response to David Cherney: Isomorphic to a pullback induced by some map. —Preceding unsigned comment added by 136.152.181.225 (talk) 02:33, 11 August 2008 (UTC)[reply]

Torus

I think we want Z^2n for the Torus of genus 'n'. - D.S. —Preceding unsigned comment added by Dhs601 (talk • contribs) 19:27, 6 November 2008 (UTC)[reply]

When people say the "n-Torus", the n refers to the dimension of the manifold, not the genus. The article as written is correct in this usage.67.198.37.16 (talk) 15:41, 26 June 2016 (UTC)[reply]

References

There is quite some material on this page, it would be nice if we could cite some references. Alvisetrevi (talk) 12:36, 16 October 2008 (UTC)[reply]

Homotopy classes of classifying maps?

If the article mentions the correspondence between homotopy classes of classifying maps and equivalence classes of bundles, I was unable to find this in the article.

But this is an important aspect of classifying spaces. I hope someone knowledgeable about this subject can fix this omission.

(Or if this is mentioned, it needs to be mentioned much more prominently, and also in the introduction.)