TOPOLOGY OF COMBINATORIAL DIFFERENTIAL MANIFOLDS

We prove that all combinatorial differential manifolds involving only Euclidean oriented matroids are PL manifolds. In doing so we introduce a new notion of triangulations of oriented matroids, cand show that any triangulation of a Euclidean oriented matroid is a PL sphere. tion 5 we adapt these results to get a new definition of triangulations of oriented matroid polytopes, and show that any triangulation of a Euclidean oriented matroid polytope is a PL ball.