S. O. Ivanov

collaborators

5 papers

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.KT2024

On diagonal digraphs, Koszul algebras and triangulations of homology spheres

Sergei O. Ivanov, Lev Mukoseev

We study magnitude homology of digraphs, with a particular focus on diagonal digraphs, i.e., digraphs whose magnitude homology is concentrated on the diagonal. For any digraph $G$ ,…

math.KT2024

Magnitude homology is a derived functor

Yasuhiko Asao, Sergei O. Ivanov

We prove that the magnitude (co)homology of an enriched category can, under some technical assumptions, be described in terms of derived functors between certain abelian categories…

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…

math.KT2023

Transfinite version of the Mittag-Leffler condition for the vanishing of the derived limit

Mishel Carelli, Sergei O. Ivanov

We give a necessary and sufficient condition for an inverse sequence $S_{0} \leftarrow S_{1} \leftarrow \dots$ indexed by natural numbers to have $lim^{1} S = 0$ . This condition can b…