S. O. Ivanov

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math.AT2024

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 $F$ , we construct a basis of the vector space of path $n$ -chains $Ω_{n} (G; F)$ for $n \geq 0$ , generalising the bas…

math.AT2023

Nested homotopy models of finite metric spaces and their spectral homology

Sergei O. Ivanov

For a real $r \geq 0,$ we consider the notion of $r$ -homotopy equivalence in the category quasimetric spaces, which includes metric spaces and directed graphs. We show that for a fi…