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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 1999
 arXiv:
 arXiv:math/9902151
 Bibcode:
 1999math......2151G
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Algebraic Topology;
 Condensed Matter  Other;
 Computer Science;
 18G;
 55U
 EPrint:
 54 pages, 1 eps figure, LaTeX2e