A directed homotopy category
Eric Goubault – 11 December 2002
This talk is a follow-up of the talk of last week, which only introduced the basic motivation for studying a form of homotopy which "does not reverse time". In this presentation, I will construct a category of globular CW-complexes, (common work with Philippe Gaucher, IRMA Strasbourg) which are to be the counterparts of the usual CW-complexes, for directed topology. These will be quickly compared with (pre-)cubical sets and local po-spaces, which are other well-known models for directed topology. Then I will define directed homotopy equivalence and consider the localization of the category of globular CW-complexes with respect to this equivalence.
Some examples will be given together with some relationships to ordinary homotopy types. I will end up by introducing a new construction of the directed homotopy category, due to Philippe Gaucher, based on a category of "flows", which forms a model category.
Refs: - Philippe Gaucher, Eric Goubault. Topological Deformation of Higher Dimensional Automata. to appear in Homology, Homotopy and Applications - Philippe Gaucher. A Convenient Category for The Homotopy Theory of Concurrency. available on ArXiv