| Homology Type | Applicability | Computation |
|---|---|---|
| Singular Homology | All topological spaces | Hard to compute |
| Simplicial Homology | Only triangulable spaces (i.e. geometric realizations ofe simplicial complexes) | Easy to compute |
CW complexes are obtained by gluing spherical cells, more general than triangulable spaces, but computation of the singular homology groups is often more tractable.