On Steenrod Operations in Oriented and Special Unitary Cobordism Theories

Algebras of Steenrod operations in oriented and special unitary cobordisms are constructed. The representing spectra of SO- and SU-cobordisms are studied. It is shown that on the corresponding spectra, there exists the structure of a multiplicative family over a suitable bioperad. The connection with Steenrod operations proposed by T. tom Dieck is established. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 19, Topology and Noncommutative Geometry, 2004.