Alexander Engström: Topological Representations of Matroids

In the theory of oriented matroids one of the basic tools is the old topological representation theorem. It was common wisdom that this couldn't be done for ordinary matroids until Ed Swartz proved that it actually could be done.

We give a conceptual new way to find topological representations of matroids. They are homotopy colimits of diagrams of spaces, and the diagrams are geometric lattices of matroids.