Geodesic
Time-reversal homotopical properties of concurrent systems
Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 31-57.

Voir la notice de l'article provenant de la source International Press of Boston

Directed topology was introduced as a model of concurrent programs, where the flow of time is described by distinguishing certain paths in the topological space representing such a program. Algebraic invariants which reflect this directedness have been introduced to classify directed spaces. In this work we study the properties of such invariants with respect to the reversal of the flow of time in directed spaces. Known invariants, natural homotopy and homology, have been shown to be unchanged under this time-reversal.We show that these can be equipped with additional algebraic structure witnessing this reversal. Specifically, when applied to a directed space and to its reversal, we show that these enhanced invariants yield dual objects. We further refine natural homotopy by introducing a notion of relative directed homotopy and showing the existence of a long exact sequence of natural homotopy systems.
DOI : 10.4310/HHA.2020.v22.n2.a2
Classification : 18D35, 55U99, 68Q85
Keywords: directed spaces, concurrent systems, time-reversibility, natural homology and natural homotopy 
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Cameron Calk; Eric Goubault; Philippe Malbos. Time-reversal homotopical properties of concurrent systems. Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 31-57. doi : 10.4310/HHA.2020.v22.n2.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n2.a2/

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