Homotopy invariants of higher dimensional categories and concurrency in computer science

Abstract

The strict globular $\omega$-categories formalize the execution paths of a parallel automaton and the homotopies between them. One associates to such (and any) $\omega$-category $\C$ three homology theories. The first one is called the globular homology. It contains the oriented loops of $\C$. The two other ones are called the negative (resp. positive) corner homology. They contain in a certain manner the branching areas of execution paths or negative corners (resp. the merging areas of execution paths or positive corners) of $\C$. Two natural linear maps called the negative (resp. the positive) Hurewicz morphism from the globular homology to the negative (resp. positive) corner homology are constructed. We explain the reason why these constructions allow to reinterprete some geometric problems coming from computer science.

54 pages, 1 eps figure, LaTeX2e ; v2 construction of negative and positive Hurewicz morphisms added, corrected reference ; v3 reorganized paper for a better understanding ; v4 final version to appear in Mathematical Structure in Computer Science ; v5 last minute correction (very minor changes)

References in corpus (1)

• The geometry of oriented cubes

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