New York Journal of Mathematics
Volume 12 (2006) 319-348


Philippe Gaucher

T-homotopy and refinement of observation. III. Invariance of the branching and merging homologies

Published: September 19, 2006
Keywords: concurrency, homotopy, directed homotopy, model category, refinement of observation, poset, cofibration, Reedy category, homotopy colimit, branching, merging, homology
Subject: 55U35, 55P99, 68Q85

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 nondeterministic 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.

Author information

Preuves Programmes et Systèmes, Université Paris 7-Denis Diderot, Case 7014, 2 Place Jussieu, 75251 PARIS Cedex 05, France