Author : Philippe Gaucher Title : A long exact sequence for the branching homology Abstract : A function complex is introduced on the category of flows so that the model category of flows becomes a simplicial model category. This allows us to show that the homotopy branching space of the cone of a morphism of flows is homotopy equivalent to the cone of its image by the homotopy branching space functor. The crux of the proof is that the homotopy branching space of the terminal flow is contractible. We then easily deduce a long exact sequence for the branching homology of a flow. Url : http://www-irma.u-strasbg.fr/~gaucher/ or Arxiv : math.AT/0305169