Circuit admissible triangulations of oriented matroids (Q1349283)

All triangulations of Euclidean oriented matroids are PL-homeomorphic to each other by a result of \textit{L. Anderson} [Topology 38, 197-221 (1999; Zbl 0924.57028)]. This paper provides a partial result for general oriented matroids. This concerns the class of circuit admissible triangulations. Roughly speaking, these are triangulations without intersection circuits, i.e., without circuits whose positive part is contained in one simplex and whose negative part is contained in another simplex of the triangulation. It is shown that for such circuit admissible triangulations the \([p_-, p_+]\)-adjacency graph is a path, a crucial condition in Anderson's proof.