preprint : Homotopy branching space and weak dihomotopy

preprint : Homotopy branching space and weak dihomotopy

[Philippe Gaucher]

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