Homology, Homotopy and Applications

Volume 7 (2005)

Number 1

Homological properties of non-deterministic branchings of mergings in higher dimensional automata

Pages: 51 – 76

DOI: https://dx.doi.org/10.4310/HHA.2005.v7.n1.a4

Author

Philippe Gaucher (Preuves Programmes et Systèmes, Université Paris 7 – Denis Diderot, Paris, France)

Abstract

The branching (resp. merging) space functor of a flow is a left Quillen functor. The associated derived functor allows to define the branching (resp. merging) homology of a flow. It is then proved that this homology theory is a dihomotopy invariant and that higher dimensional branchings (resp. mergings) satisfy a long exact sequence.

Keywords

concurrency, homotopy, branching, merging, homology, left Quillen functor, long exact sequence, Mayer-Vietoris, cone, higher dimensional automata, directed homotopy

2010 Mathematics Subject Classification

55N35, 55P99, 68Q85

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Published 1 January 2005