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

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dc.creatorGaucher, Philippe
dc.date2005-05-16
dc.date2007-03-26
dc.date.accessioned2026-07-07T08:06:54Z
dc.date.available2026-07-07T08:06:54Z
dc.descriptionThis 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.
dc.description20 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0505328
dc.identifierhttp://arxiv.org/abs/math/0505328
dc.identifierInternational Journal of Mathematics and Mathematical Sciences, Article ID 87404, 20 pages, 2007
dc.identifierdoi:10.1155/2007/87404
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130764
dc.subjectAlgebraic Topology
dc.subjectCategory Theory
dc.subject55U35 ; 55P99 ; 68Q85
dc.titleT-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences
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