29 citations · 187 across the 52 of their papers we have counts for
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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…
HR-length of a free group via polynomial functors
Sergei O. Ivanov, Roman Mikhailov
We prove that for a subring and a free group of rank at least the length of the Bousfield's -localization tower for is at least . The ke…
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…
Homology of the pronilpotent completion and cotorsion groups
Mikhail Basok, Sergei O. Ivanov, Roman Mikhailov
For a non-cyclic free group , the second homology of its pronilpotent completion is not a cotorsion group.
On the cokernel of the Baumslag rationalization
Sergei O. Ivanov
We prove that for the free group of rank two the cokernel of the homomorphism to its Baumslag rationalization is not abelian. Moreover, this cokernel contai…
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…