T-Homotopy and Refinement of Observation, Part II: Adding New T-Homotopy Equivalences

Philippe Gaucher (1)

1 PPS - Preuves, Programmes et Systèmes

This paper is the second part of a series of papers about a new notion of T-homotopy of flows. 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 contradicts 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. The left-properness of the weak S-homotopy model category of flows is also established in this second part. The latter fact is used several times in the next papers of this series.

Domaines: Topologie algébrique [math.AT]; Catégories et ensembles [math.CT]

Philippe Gaucher. T-Homotopy and Refinement of Observation, Part II: Adding New T-Homotopy Equivalences. International Journal of Mathematics and Mathematical Sciences, 2007, 2007, Article ID 87404, 20 p. ⟨10.1155/2007/87404⟩. ⟨hal-00150917⟩