2019
Том 71
№ 11

# Kolesnyk P. O.

Articles: 2
Article (English)

### Atoms in the p-localization of Stable Homotopy Category

Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 458–472

We study p-localizations, where p is an odd prime, of the full subcategories ${\mathcal{S}}^n$ of stable homotopy category formed by CW-complexes with cells in n successive dimensions. Using the technique of triangulated categories and matrix problems, we classify the atoms (indecomposable objects) in ${\mathcal{S}}_p^n$ for n ≤ 4(p − 1) and show that, for n > 4(p − 1), this classification is wild in a sense of the representation theory.

Article (English)

### Genera of the Torsion-Free Polyhedra

Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1332–1341

We study the genera of polyhedra (finite cell complexes), i.e., the classes of polyhedra such that all their localizations are stably homotopically equivalent. More precisely, we describe the genera of the torsion-free polyhedra of dimensions not greater than 11. In particular, we find the number of stable homotopy classes in these genera.