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math.AT2023
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…
math.AT2022★ 3 cited
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…
math.AT2017★ 2 cited
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…