From Concurrency to Algebraic Topology

AbstractThis paper is a survey of the new notions and results scattered in [13,11,12]. However the speculations of Section 5 and Section 6 are new. Starting from a formalization of higher dimensional automata (HDA) by strict globular ω-categories, the construction of a diagram of simplicial sets over the three-object small category − ← gl → + is exposed. Some of the properties discovered so far on the corresponding simplicial homology theories are explained, in particular their links with geometric problems coming from concurrency theory in computer science