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What does this diagram do for us?

Time for a big word: Naturality of the long exact sequence in homology and commutativty of the diagram shown means that not only will the map $f$ descend to the homology groups but it will descend in such a way that the diagram below will be commutative.

\cdots \ar[r] & H_n(A) \ar[r] \ar[d]_{f_\ast} & H_...
...{X}) \ar[r] & H_n(\overline{X}, \overline{A}) \ar[r] & \cdots

Christine Devena 2003-07-25