29 citations · 187 across the 52 of their papers we have counts for
10 papers · 1 filter
On the path homology of Cayley digraphs and covering digraphs
Shaobo Di, Sergei O. Ivanov, Lev Mukoseev +1
We develop a theory of covering digraphs, similar to the theory of covering spaces. By applying this theory to Cayley digraphs, we build a "bridge" between GLMY-theory and group ho…
Simplicial approach to path homology of quivers, marked categories, groups and algebras
Sergei O. Ivanov, Fedor Pavutnitskiy
We develop a generalisation of the path homology theory introduced by Grigor'yan, Lin, Muranov and Yau (GLMY-theory) in a general simplicial setting. The new theory includes as par…
An overview of rationalization theories of non-simply connected spaces and non-nilpotent groups
Sergei O. Ivanov
We give an overview of five rationalization theories for spaces (Bousfield-Kan's -completion; Sullivan's rationalization; Bousfield's homology rationalization; Casacuber…
Baumslag rationalization of spaces
Sergei O. Ivanov
Using the functor of Baumslag rationalization of groups we construct a functor on the category of all (non necessarily simply connected) spaces that extends the classical rationali…
A Simple proof of Curtis' connectivity theorem for Lie powers
Sergei O. Ivanov, Vladislav Romanovskii, Andrei Semenov
We give a simple proof of the Curtis' theorem: if is -connected free simplicial abelian group, then is an -connected simp…
Right exact group completion as a transfinite invariant of the homology equivalence
Sergei O. Ivanov, Roman Mikhailov
We consider a functor from the category of groups to itself that we call right exact -completion of a group. It is connected with the proni…