4 citations · 11 across the 9 of their papers we have counts for
9 papers
-weight system does not extend to a graph 4-invariant
Daniil Fomichev, Maksim Karev, Fedor Pavutnitskiy +1
A long-standing question by S. Lando asks whether the -weight system extends to a unique 4-invariant of graphs. We show that, in full generality, the answer to th…
Limits via relations
Sergei O. Ivanov, Roman Mikhailov, Fedor Pavutnitskiy
In this paper, we study operations on functors in the category of abelian groups simplar to the derivation in the sense of Dold-Puppe. They are defined as derived limits of a funct…
Applying language models to algebraic topology: generating simplicial cycles using multi-labeling in Wu's formula
Kirill Brilliantov, Fedor Pavutnitskiy, Dmitry Pasechnyuk +1
Computing homotopy groups of spheres has long been a fundamental objective in algebraic topology. Various theoretical and algorithmic approaches have been developed to tackle this…
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…
Quadric Hypersurface Intersection for Manifold Learning in Feature Space
Fedor Pavutnitskiy, Sergei O. Ivanov, Evgeny Abramov +5
The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark an…
On homology of Lie algebras over commutative rings
Sergei O. Ivanov, Fedor Pavutnitskiy, Vladislav Romanovskii +1
We study five different types of the homology of a Lie algebra over a commutative ring which are naturally isomorphic over fields. We show that they are not isomorphic over commuta…
Limits, standard complexes and fr-codes
Sergei O. Ivanov, Roman Mikhailov, Fedor Pavutnitskiy
For a strongly connected category with pair-wise coproducts, we introduce a cosimplicial object, which serves as a sort of resolution for computing higher derived func…
Right exact localizations of groups
Danil Akhtiamov, Sergei O. Ivanov, Fedor Pavutnitskiy
We introduce several classes of localizations (idempotent monads) on the category of groups and study their properties and relations. The most interesting class for us is the class…
Simplicial James-Hopf map and decompositions of the unstable Adams spectral sequence for suspensions
Fedor Pavutnitskiy, Jie Wu
We use combinatorial group theory methods to extend the definition of a classical James-Hopf invariant to a simplicial group setting. This allow us to realize certain coalgebra ide…