categories: preprint: Combinatorics of branchings in higher dimensional automata

[Philippe Gaucher <gaucher@irmast1.u-strasbg.fr>]

Title : Combinatorics of branchings in higher dimensional automata

Abstract :

We explore the combinatorial properties of the branching areas of 
paths in higher dimensional automata. Mathematically, this means 
that we investigate the combinatorics of the negative corner homology 
of a globular $\omega$-category and the combinatorics of a new homology 
theory called the reduced negative corner homology. This latter is the 
homology of the quotient of the corner complex by the sub-complex 
generated by its thin elements. As application, we calculate the corner 
homology of some $\omega$-categories and we give some invariance results 
for the reduced corner homology. We only treat the negative side. The 
positive side, that is to say the case of merging areas of paths is 
similar and can be easily deduced from the negative side. 

URL : math.CT/9912059 (XXX archive http://arXiv.org/)

Comments : LaTeX2e, 42 pages