# Request: intermediate-level proof: every 2-homology class of a 4-manifold is generated by a surface.

Hi, everyone:

For the sake of context, I am a graduate student, and I have taken classes in algebraic topology and differential geometry. Still, the 2 proofs I have found are a little too terse for me; they are both around 10 lines long, and each line seems to pack around 10 pages of results. Of course, I am considering cases for "reasonable" spaces, being the beginner I am at this point.

It would also be great if someone knew of similar results for H_1 (equiv. H_3).

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Thanks, but this is a different question from the one you are referring/linking to. The only thing common to both is that both questions are on, or relate-to, 4-manifolds. AFAIK, the intersection form assumes the existence of representative surfaces, but does not prove their existence. An etiquette question: I was able to answer my own previous question, the one you linked to. But since I saw it was of such low interest in this site, I thought I would not comment on this. Is that O.K in this site.? –  Herb Apr 25 '10 at 1:35
Herb: my mistake regarding the question -- I read too hastily, and will delete my comments. As for the etiquette question: if you were able to answer a question you posed then I think it is preferred that you add a comment to that effect; you're even allowed to post an answer yourself and accept it. This is because open questions get sporadically and automatically bumped to the top by the software, so it's still worth updating or correcting them. –  Yemon Choi Apr 25 '10 at 1:41