Spaces of directed paths on pre-cubical sets
Algebraic Topology
2016-05-27 v1
Abstract
The spaces of directed paths on the geometric realizations of pre-cubical sets, called also --sets, can be interpreted as the spaces of possible executions of Higher Dimensional Automata, which are models for concurrent computations. In this paper we construct, for a sufficiently good pre-cubical set , a CW-complex that is homotopy equivalent to the space of directed paths between given vertices , of . This construction is functorial with respect to , and minimal among all functorial constructions. Furthermore, explicit formulas for incidence numbers of the cells of are provided.
Cite
@article{arxiv.1605.08305,
title = {Spaces of directed paths on pre-cubical sets},
author = {Krzysztof Ziemiański},
journal= {arXiv preprint arXiv:1605.08305},
year = {2016}
}