AbstractWe introduce the notion of a d-simplicial complex — a directed analogue of a simplicial complex. Then we construct a pre-cubical model for the space of paths between two vertices of a finite d-simplicial complex K. Next, we prove that (if K has no directed loops) this model is actually homotopy equivalent to the space of paths
AbstractIn the geometric realization of a cubical complex without degeneracies, a □-set, dipaths and...
Abstract. We prove several combinatorial results on path algebras over discrete structures related t...
We construct a functor associating a cubical set to a (simple) graph. We show that cubical sets aris...
AbstractWe introduce the notion of a d-simplicial complex — a directed analogue of a simplicial comp...
Directed algebraic topology studies topological spaces in which certain directed paths (d-paths) are...
In directed algebraic topology, directed irreversible (d)-paths and spaces consisting of d-paths are...
AbstractIn directed algebraic topology, directed irreversible (d)-paths and spaces consisting of d-p...
Abstract. Topological spaces- such as classifying spaces, configuration spaces and spacetimes- often...
In directed algebraic topology, (spaces of) directed irreversible (d)-paths are studied from a topol...
22 pagesUsing the notion of regular d-path of the topological n-cube, we construct the regular reali...
20 pagesA flow is a directed space structure over a homotopy type. It is already known that the unde...
Grigoryan A, Muranov Y. On homology theories of cubical digraphs. Pacific Journal of Mathematics. 20...
Directed Algebraic Topology studies topological spaces in which certain directed paths (d-paths) - i...
Thesis (Ph.D.)--University of Washington, 2023This thesis consists of three papers about cubical com...
The identification of morphism sets in path categories of simplicial (or cubical) complexes is a cen...
AbstractIn the geometric realization of a cubical complex without degeneracies, a □-set, dipaths and...
Abstract. We prove several combinatorial results on path algebras over discrete structures related t...
We construct a functor associating a cubical set to a (simple) graph. We show that cubical sets aris...
AbstractWe introduce the notion of a d-simplicial complex — a directed analogue of a simplicial comp...
Directed algebraic topology studies topological spaces in which certain directed paths (d-paths) are...
In directed algebraic topology, directed irreversible (d)-paths and spaces consisting of d-paths are...
AbstractIn directed algebraic topology, directed irreversible (d)-paths and spaces consisting of d-p...
Abstract. Topological spaces- such as classifying spaces, configuration spaces and spacetimes- often...
In directed algebraic topology, (spaces of) directed irreversible (d)-paths are studied from a topol...
22 pagesUsing the notion of regular d-path of the topological n-cube, we construct the regular reali...
20 pagesA flow is a directed space structure over a homotopy type. It is already known that the unde...
Grigoryan A, Muranov Y. On homology theories of cubical digraphs. Pacific Journal of Mathematics. 20...
Directed Algebraic Topology studies topological spaces in which certain directed paths (d-paths) - i...
Thesis (Ph.D.)--University of Washington, 2023This thesis consists of three papers about cubical com...
The identification of morphism sets in path categories of simplicial (or cubical) complexes is a cen...
AbstractIn the geometric realization of a cubical complex without degeneracies, a □-set, dipaths and...
Abstract. We prove several combinatorial results on path algebras over discrete structures related t...
We construct a functor associating a cubical set to a (simple) graph. We show that cubical sets aris...
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