Author : Philippe Gaucher Title : Homotopy branching space and weak dihomotopy Abstract : The branching space of a flow is the topological space of germs of its non-constant execution paths beginning in the same way. However, there exist weakly S-homotopy equivalent flows having non weakly homotopy equivalent branching spaces. This topological space is then badly behaved from a computer-scientific viewpoint since weakly S-homotopy equivalent flows must correspond to higher dimensional automata having the same computer-scientific properties. To overcome this problem, the homotopy branching space of a flow is introduced as the left derived functor of the branching space functor from the model category of flows to the model category of topological spaces. As an application, we use this new functor to correct the notion of weak dihomotopy equivalence, which did not identify enough flows in its previous version. Comments : 44 pages, 3 figures Url : http://www-irma.u-strasbg.fr/~gaucher/ or Arxiv : math.AT/0304112