On the properties of the cobordism group of stably-framed immersions in codimension $k$

P. M. Akhmet'ev<sup>ab

a</sup> Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moskovskaya obl.
^b HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE), School of Applied Mathematics (Moscow)

Abstract: The notion “intermediate bordism group”, which was introduced by P. J. Eccles to investigate filtrations in stable homotopy group of spheres, is considered. А new notion “cobordism groups of stable-framed immersions” is introduced. The classifying space for the new groups is constructed, ranks of the groups are calculated. Hopf invariants and the Kahn-Priddy homomorphism are generalized for cobordism groups of stable-framed immersions.

Keywords: stable homotopy groups of spheres, immersion.

UDC: 515.146.6+515.164.635

Received: 25.12.2019
Accepted: 11.03.2020

DOI: 10.22405/2226-8383-2018-21-2-26-36