  The homological information about a filtered simplicial complex over the
poset of positive real numbers is often presented by a barcode which depicts
the evolution of the associated Betti numbers. However, there is a wonderfully
complex combinatorics associated with the homology classes of a filtered
complex, and one can do more than just counting them over the index poset.
Here, we show that this combinatorial information can be encoded by filtered
matroids, or even better, by rooted forests. We also show that these rooted
forests can be realized as cobordisms.
