Dear categorists, Here are five new preprints. The fith one is actually an updated version of a "old" thing with an application added. Url : ArXiv and http://www.pps.jussieu.fr/~gaucher/ Sincerely yours. pg. ------------------------------------------------------------------------------------------------------------------ Title: T-homotopy and refinement of observation (I) : Introduction Author: Philippe Gaucher Abstract: This paper is the extended introduction of a serie of papers about modelling T-homotopy by refinement of observation. The notion of T-homotopy equivalence is discussed. A new one is proposed and its behaviour with respect to other construction in dihomotopy theory is explained. ------------------------------------------------------------------------------------------------------------------ Title: T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences Author: Philippe Gaucher Abstract: It is proved that the old definition of T-homotopy equivalence does not allow the identification of the directed segment with the $3$-dimensional cube. This contredicts a paradigm of dihomotopy theory. A new definition of T-homotopy equivalence is proposed, following the intuition of refinement of observation. And it is proved that up to weak S-homotopy, a old T-homotopy equivalence is a new T-homotopy equivalence. ------------------------------------------------------------------------------------------------------------------ Title: T-homotopy and refinement of observation (III) : Invariance of the branching and merging homologies Author: Philippe Gaucher Abstract: It is proved that the generalized T-homotopy equivalences preserve the branching and merging homology theories of a flow. ------------------------------------------------------------------------------------------------------------------ Title: T-homotopy and refinement of observation (IV) : Invariance of the underlying homotopy type Author: Philippe Gaucher Abstract: It is proved that the generalized T-homotopy equivalences preserve the underlying homotopy type of a flow. ------------------------------------------------------------------------------------------------------------------ Title: T-homotopy and refinement of observation (V) : Strom model structure for branching and merging homologies Author: Philippe Gaucher Abstract: We check that there exists a model structure on the category of flows whose weak equivalences are the S-homotopy equivalences. As an application, we prove that the generalized T-homotopy equivalences preserve the branching and merging homology theories of a flow. The method of proof is completely different from the one of the third part of this series of papers. ------------------------------------------------------------------------------------------------------------------ 16-May-2005 15:02:53 -0300,5422;000000000000-00000007