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 Mat. Zametki, 2008, Volume 84, Issue 5, Pages 763–771 (Mi mz4055)

Bott's Periodicity Theorem and Differentials of the Adams Spectral Sequence of Homotopy Groups of Spheres

V. A. Smirnov

Moscow State Pedagogical University

Abstract: Bott's periodicity theorem is applied to calculate higher-order differentials of the Adams spectral sequence of homotopy groups $\pi_*(SO)$. The resulting formulas are used to find higher-order differentials of the Adams spectral sequence of homotopy groups of spheres.

Keywords: Bott's periodicity theorem, differentials of the Adams spectral sequence, homotopy groups of spheres, stable homotopy group, exterior algebra, loop space

DOI: https://doi.org/10.4213/mzm4055

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English version:
Mathematical Notes, 2008, 84:5, 710–717

Bibliographic databases:

UDC: 513.83

Citation: V. A. Smirnov, “Bott's Periodicity Theorem and Differentials of the Adams Spectral Sequence of Homotopy Groups of Spheres”, Mat. Zametki, 84:5 (2008), 763–771; Math. Notes, 84:5 (2008), 710–717

Citation in format AMSBIB
\Bibitem{Smi08} \by V.~A.~Smirnov \paper Bott's Periodicity Theorem and Differentials of the Adams Spectral Sequence of Homotopy Groups of Spheres \jour Mat. Zametki \yr 2008 \vol 84 \issue 5 \pages 763--771 \mathnet{http://mi.mathnet.ru/mz4055} \crossref{https://doi.org/10.4213/mzm4055} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2500642} \elib{http://elibrary.ru/item.asp?id=13597587} \transl \jour Math. Notes \yr 2008 \vol 84 \issue 5 \pages 710--717 \crossref{https://doi.org/10.1134/S0001434608110126} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000262855600012} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-59749086617} 

• http://mi.mathnet.ru/eng/mz4055
• https://doi.org/10.4213/mzm4055
• http://mi.mathnet.ru/eng/mz/v84/i5/p763

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This publication is cited in the following articles:
1. Smirnov V. A., “Differentials of the Adams spectral sequence and the Kervaire invariant”, Dokl. Math., 80:1 (2009), 573
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