T-homotopy and refinement of observation (IV) : Invariance of the underlying homotopy type

Details T-homotopy and refinement of observation (IV) : Invariance of the underlying homotopy type T-homotopy and refinement of observation (IV) : Invariance of the underlying homotopy type

2005-05-16

arxiv.org/abs/math/0505331v3

New-York Journal of Mathematics, vol. 12 : p. 63-95, 2006

Mathematics

Algebraic Topology

33 pages ; 2 figures ; see http://nyjm.albany.edu:8000/j/2006/Vol12.htm

Scientific paper

This series explores a new notion of T-homotopy equivalence of flows. The new definition involves embeddings of finite bounded posets preserving the bottom and the top elements and the associated cofibrations of flows. In this fourth part, it is proved that the generalized T-homotopy equivalences preserve the underlying homotopy type of a flow. The proof is based on Reedy model category techniques.

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