Not sure about geometric algebra, but topology comes up because it studies the abstract formal structure that connects your problem with other (possibly solved) problems.

For example, a couple weeks ago I was musing about optimal vertex renumberings so that "the (0/1) adjacency matrix of a non-densely-connected acyclic digraph's transitive closure" scores well according to a domain-specific compressibility metric.

Specifically, at column i and row j is a 1 if and only if (using the post-remumbering indices) vertex i was reachable from vertex j in the original input graph.

The compression results from only storing start and end indices of contiguous runs of 1s in a row. [Edit2: the score of a specific vertex renumbering is the the number of such runs for the complete matrix. Only uninterrupted runs of 1's count.] It is easy to see that a renumbering that results in a triangular matrix won't be terrible, and simple deepest-branch-first depth-first enumeration of the input DAG's undirected "version" (one just ignores edge direction for this step) is at least fairly good for sub-quadratic in vertex count (assuming an average degree much smaller than the number of vertices).

[Edit1: I forgot to point out that this is extremely close to plain run-length-encoding of the matrix in row-major order, except for the fact that RLE cares about a row-crossing run and I don't.]

But exhaustive renumbering testing is O(n!) for n vertices.

I think topology could help me, but I'd need to know some topology to find me way around the literature.