Triangulations of Conal Manifolds

Abstract

Casual structure can take the form of cone bundles on a manifold, more general local preorders on a topological space, or simplicial orientations implicit in a simplicial set. This note takes a triangulation of a conal manifold M to mean an isomorphism between M and the locally preordered geometric realization of a simplicial set. Such triangulations completely encode causal and topological structure combinatorially. This note characterizes the triangulability of closed conal manifolds as the fibrewise freeness and generativity of the cone bundle.