Simplicial cells in arrangements and mutations of oriented matroids

Abstract

We investigate the combinatorial and topological properties of simplicial cells in arrangements of (pseudo)hyperplanes, using their interpretations in terms of oriented matroids. Simplicial cells have various applications in computational geometry due to the fact that for an arrangement in general position they are in one-to-one correspondence to local changes (‘mutations’) of its combinatorial type. Several characterizations for mutations of oriented matroids, and their relation to geometric realizability questions are being discussed.