Gottlieb Groups of Spheres

Marek Golasiński and Juno Mukai
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Marek Golasiński: Casimir the Great University, Institute of Mathematics
Juno Mukai: Shinshu University

Chapter Chapter 1 in Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces, 2014, pp 1-48 from Springer

Abstract: Abstract This chapter published in [20] takes up the systematic study of the Gottlieb groups G n + k ( 𝕊 n ) $$G_{n+k}(\mathbb{S}^{n})$$ of spheres for k ≤ 13 by means of the classical homotopy theory methods. We fully determine the groups G n + k ( 𝕊 n ) $$G_{n+k}(\mathbb{S}^{n})$$ for k ≤ 13 except for the two-primary components in the cases: k = 9 , n = 53 ; k = 11 , n = 115 $$k = 9,n = 53;k = 11,n = 115$$ . Especially, we show that [ ι n , η n 2 σ n + 2 ] = 0 $$[\iota _{n},\eta _{n}^{2}\sigma _{n+2}] = 0$$ if n = 2 i − 7 $$n = 2^{i} - 7$$ for i ≥ 4.

Keywords: Gottlieb Group; Toda Bracket; Coextension; Homotopy Groups; Cofiber Sequence (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-11517-7_1

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DOI: 10.1007/978-3-319-11517-7_1

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