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Chebyshevskii Sbornik, 2020, Volume 21, Issue 2, Pages 26–36
DOI: https://doi.org/10.22405/2226-8383-2018-21-2-26-36 (Mi cheb893) 		 
On the properties of the cobordism group of stably-framed immersions in codimension $k$

P. M. Akhmet'evab

a 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)
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DOI: https://doi.org/10.22405/2226-8383-2018-21-2-26-36
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.
Received: 25.12.2019
Accepted: 11.03.2020
Document Type: Article
UDC: 515.146.6+515.164.635
Language: Russian
Citation: P. M. Akhmet'ev, “On the properties of the cobordism group of stably-framed immersions in codimension $k$”, Chebyshevskii Sb., 21:2 (2020), 26–36
Citation in format AMSBIB
\Bibitem{Akh20}
\by P.~M.~Akhmet'ev
\paper On the properties of the cobordism group of stably-framed immersions in codimension~$k$
\jour Chebyshevskii Sb.
\yr 2020
\vol 21
\issue 2
\pages 26--36
\mathnet{http://mi.mathnet.ru/cheb893}
\crossref{https://doi.org/10.22405/2226-8383-2018-21-2-26-36}
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