No that ' s a bad deal for me <| sep |> Once people get into these subjects to a certain level , they usually find that topology is ' hard ' while algebra is ' easy ', relatively speaking . Algebraic topology is all about solving problems in topology by translating them into problems about algebra . The two simplest ways to do this are with the fundamental group and the homology groups . Setting these up takes some work . But once you get past that , very beautiful theorems result . You can prove that two topological spaces are not homeomorphic because if they were their fundamental groups or homology groups would be isomorphic . That ' s because fundamental group and homology are functors , a really important concept . For example , the fundamental group of the ordinary 2 dimensional sphere S 2 is 0 , but that of the torus is Z x Z , so they can ' t be homeomorphic .