Hi, everyone: I wonder if anyone knows the actual definition of having a surface represent a homology class. Sorry to bother with just a definition, but I have not been able to find one , neither in books nor online. I am reading that a certain surface represents H_2(M,Z) , the second homology class of an orientable manifold. All I can see is mention of the inclusion map (and its pushforward), and the fundamental class ( a generator of top homology). Anyone know the def., or can give me a link/reference? Thanks.