T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences

Details T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences

2005-05-16

arxiv.org/abs/math/0505328v3

International Journal of Mathematics and Mathematical Sciences, Article ID 87404, 20 pages, 2007

Mathematics

Algebraic Topology

20 pages, 3 figures

Scientific paper

10.1155/2007/87404

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.

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