I was studying simplicial homology in Hatcher's Algebraic topology book.In one paragraph book says following: Some obvious general questions arise: Are the groups $H_n(X)$ independent of the choice of simplicial complex structure on X? In other words, if two complexes are homeomorphic, do they have isomorphic homology groups? More generally, do they have isomorphic homology groups if they are merely homotopy equivalent? To answer such questions and to develop a general theory it is best to leave the rather rigid simplicial realm and introduce the singular homology groups.
My Question is what is the answers of the above mentioned questions?? any help would be appreciated.