On nontriviality of certain homotopy groups of spheres

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On nontriviality of certain homotopy groups of spheres. / Ivanov, Sergei O.; Mikhailov, Roman; Wu, Jie.

In: Homology, Homotopy and Applications, Vol. 18, No. 2, 01.01.2016, p. 337-344.

Research output: Contribution to journal › Article › peer-review

Author

Ivanov, Sergei O. ; Mikhailov, Roman ; Wu, Jie. / On nontriviality of certain homotopy groups of spheres. In: Homology, Homotopy and Applications. 2016 ; Vol. 18, No. 2. pp. 337-344.

BibTeX

@article{a38e7ed73ad446178d9b27c0fbc2decd,

title = "On nontriviality of certain homotopy groups of spheres",

abstract = "We provide an alternative proof of Gray's result that, for an odd prime p, there is a non-trivial Z/p-component in the homotopy group π(2p-2)n+1(S3). As a corollary, it follows that, for n ≥ 2, the homotopy groups πn(S2) are non-zero.",

keywords = "Homotopy group, Lambda algebra, Toda element",

author = "Ivanov, {Sergei O.} and Roman Mikhailov and Jie Wu",

year = "2016",

month = jan,

day = "1",

doi = "10.4310/HHA.2016.v18.n2.a18",

language = "English",

volume = "18",

pages = "337--344",

journal = "Homology, Homotopy and Applications",

issn = "1532-0073",

publisher = "International Press of Boston, Inc.",

number = "2",

}

RIS

TY - JOUR

T1 - On nontriviality of certain homotopy groups of spheres

AU - Ivanov, Sergei O.

AU - Mikhailov, Roman

AU - Wu, Jie

PY - 2016/1/1

Y1 - 2016/1/1

N2 - We provide an alternative proof of Gray's result that, for an odd prime p, there is a non-trivial Z/p-component in the homotopy group π(2p-2)n+1(S3). As a corollary, it follows that, for n ≥ 2, the homotopy groups πn(S2) are non-zero.

AB - We provide an alternative proof of Gray's result that, for an odd prime p, there is a non-trivial Z/p-component in the homotopy group π(2p-2)n+1(S3). As a corollary, it follows that, for n ≥ 2, the homotopy groups πn(S2) are non-zero.

KW - Homotopy group

KW - Lambda algebra

KW - Toda element

UR - http://www.scopus.com/inward/record.url?scp=85046134189&partnerID=8YFLogxK

U2 - 10.4310/HHA.2016.v18.n2.a18

DO - 10.4310/HHA.2016.v18.n2.a18

M3 - Article

AN - SCOPUS:85046134189

VL - 18

SP - 337

EP - 344

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

SN - 1532-0073

IS - 2

ER -

ID: 46234432