# 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).