# Homotopy invariants of higher dimensional categories and concurrency in computer science

@article{Gaucher1999HomotopyIO, title={Homotopy invariants of higher dimensional categories and concurrency in computer science}, author={Philippe Gaucher}, journal={Mathematical Structures in Computer Science}, year={1999}, volume={10}, pages={481 - 524} }

The strict globular ω-categories formalize the execution paths of a parallel automaton and the homotopies between them. One associates to such (and any) ω-category [Cscr ] three homology theories. The first one is called the globular homology. It contains the oriented loops of [Cscr ]. The two other ones are called the negative (respectively, positive) corner homology. They contain in a certain manner the branching areas of execution paths or negative corners (respectively, the merging areas of…

## 63 Citations

### Combinatorics of branchings in higher dimensional automata

- MathematicsArXiv
- 1999

The combinatorial properties of the branchingareas of execution paths in higher dimensional automata are explored and the branchinghomolog y of some ω- categories is calculated and some invariance results for the reduced branching homology are given.

### Topological deformation of higher dimensional automata

- Mathematics, Computer Science
- 2001

The category of globular CW-complexes is introduced, which provides a rigorous mathematical foundation to study from an algebraic topology point of view higher dimensional automata and concurrent computations.

### SOME GEOMETRIC PERSPECTIVES IN CONCURRENCY THEORY

- Mathematics, Computer Science
- 2003

This paper gives a survey of “geometric” models for concurrency, and develops some of the geometric intuition behind this theory and gives some hints about the algebraic objects one can associate with it (in particular homology groups).

### On the Cubical Homology Groups of Free Partially Commutative Monoids

- Mathematics
- 2006

We study a Leech homology of a locally bounded free partially commutative monoid M(E, I). Given a contravariant natural system of abelian groups F on M(E, I) we build a precubical set T(E, I) with a…

### Directed Algebraic Topology: Models of Non-Reversible Worlds

- Mathematics
- 2009

This is the first authored book to be dedicated to the new field of directed algebraic topology that arose in the 1990s, in homotopy theory and in the theory of concurrent processes. Its general aim…

### A T ] 2 4 Ju l 2 00 2 Topological Deformation of Higher Dimensional Automata

- Mathematics, Computer Science
- 2008

A particular kind of local po-space is introduced, the “globular CW-complexes”, for which these notions of deformations are formalized and which are sufficient to formalize higher dimensional automata.

### A T ] 8 J ul 2 00 1 Topological Deformation of Higher Dimensional Automata

- Mathematics, Computer Science
- 2001

Globular CW-complexes provide a rigorous mathematical foundation to study from an algebraic topology point of view higher dimensional automata and concurrent computations.

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