Spaces of directed paths on pre-cubical sets

2016/05/26 by Ziemiański, Krzysztof · 1 citation
#55U05 #68Q99 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.08305

Abstract

The spaces of directed paths on the geometric realizations of pre-cubical sets, called also \square--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 K, a CW-complex W(K)_v^w that is homotopy equivalent to the space of directed paths between given vertices v, w of K. This construction is functorial with respect to K, and minimal among all functorial constructions. Furthermore, explicit formulas for incidence numbers of the cells of W(K)_v^w are provided.

Cited by

• Branching space of precubical set

Related

• Spaces of directed paths on pre-cubical sets II
• Directed path spaces via discrete vector fields
• Configuration spaces and directed paths on the final precubical set
• Directed homotopy theory, I. The fundamental category
• Towards Directed Collapsibility