Triangulations of Conal Manifolds

2019/09/04 by Krishnan, Sanjeevi
#06F99 #54E99 #83C27 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #General Topology (math.GN) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1909.01971

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.

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