T-homotopy and refinement of observation (III) : Invariance of the branching and merging homologies

Details T-homotopy and refinement of observation (III) : Invariance of the branching and merging homologies T-homotopy and refinement of observation (III) : Invariance of the branching and merging homologies

2005-05-16

arxiv.org/abs/math/0505329v3

New-York Journal of Mathematics, vol. 12 : p. 319-348, 2006

Mathematics

Algebraic Topology

30 pages ; final preprint version before publication ; 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 third part, it is proved that the generalized T-homotopy equivalences preserve the branching and merging homology theories of a flow. These homology theories are of interest in computer science since they detect the non-deterministic branching and merging areas of execution paths in the time flow of a higher dimensional automaton. The proof is based on Reedy model category techniques.

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