On the topology of the combinatorial flag varieties (Q1597664)

The main result of this article is to show that the simplicial complex of all chains of matroids of a Coxeter group is shellable. This proves and extends a conjecture of White. A significant portion of the article is devoted to explaining briefly the concept of a Coxeter matroid, and developing certain theoretical tools required for the proof of the main theorem. The article also gives some results about the cohomology groups of certain other complexes.