The $i$-th homology of a complex $C$ is the quotient (ker dd^C_i/image dd^C_(i+1)).
The first example is the complex associated to a triangulation of the real projective plane, having 6 vertices, 15 edges, and 10 triangles.
|
|
|
|
|
|
|
|
The $i$-th cohomology of a complex $C$ is the $(-i)$-th homology of $C$.
|
|
|
|
|
|