Path homology of digraphs without multisquares and its comparison with homology of spaces

Xin Fu, Sergei O. Ivanov

For a digraph $G$ without multisquares and a field $\mathbb{F}$, we construct a basis of the vector space of path $n$-chains ${\Omega }_n(G;\mathbb{F})$ for $n\ge 0$, generalising the bas…