... matroid bundles. Theorem 1.1 tells us that the theory of matroid bundlesis actually the same as the theory of ordinary vector bundles. The natural source for matroid bundles lies in the world of ... that the map THE HOMOTOPY TYPE OF THE MATROID GRASSMANNIAN 945π|A: A →X is a homotopy equivalence; the base case of this inductionis simply the fact that D1, ,k∼=E1, ,k∼=∗, the ... element other than the obligatory + in the (dj,j) slot forall j =1, ,k is a + (resp. −)inthe (c, i) slot. ThenS+=A≥A+τ−1(A)andS−=A≥A−τ−1(A).Annals of Mathematics The...