Genera of the Torsion-Free Polyhedra
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.
English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 10, pp 1479-1489.
Citation Example: Kolesnyk P. O. Genera of the Torsion-Free Polyhedra // Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1332–1341.