Hi, everyone: A couple of questions, please: 1) Examples of representative surfaces or curves: Please let me know if this is a correct definition of a surface representing H_2(M;Z): Let M be an orientable m-manifold, Z the integers; m>2 . Let S be an orientable surface embedded in M. Then H_2(S;Z)=Z . We then say that S represents H_2(M;Z)~Z if the homomorphism h: Z-->H_2(M;Z) sends 1 --as a generator of Z -- to the homology class of S. specifically, if we have h(1)=alpha ; alpha a homology class, then there is an embedding i:S-->M , with [i(S)] =alpha. If this is correct. Anyone know of examples of representative curves or surfaces.? 2)An argument for why non-orientable manifolds have top homology zero, and for why orientable manifolds have top homology class Z.?. I have no clue on this one. I know homology zero means that all cycles are boundaries, but I don't see how this is equivalent to not being orientable. Thanks in Advance.