Geodesic
Generalized Gottlieb and Whitehead center groups of space forms
Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 323-340.

Voir la notice de l'article provenant de la source International Press of Boston

We extend Oprea’s result that the Gottlieb group $G_1(\mathbb{S}^{2n+1}/H)$ is $\mathcal{Z}H$ (the center of $H$) and show that for a map $f : A \to \mathbb{S}^{2n+1}/H$, under some conditions on $A$, we have $G^f_1 (\mathbb{S}^{2n+1} / H)=\mathcal{Z}_H f_{*} (\pi_1(A))$, the centralizer of the image $f_{*} (\pi_1(A))$ in $H$. Then, we compute or estimate the groups $G^f_m (\mathbb{S}^{2n+1}/H)$ and $P^f_m (\mathbb{S}^{2n+1} / H)$ for certain $m \gt 1$.
DOI : 10.4310/HHA.2019.v21.n1.a15
Classification : 55Q15, 55Q52, 55R05, 57S17
Keywords: classifying space, Gottlieb group, homology group, homotopy group, Moore–Postnikov tower, $n$-equivalence, projective space, space form, Whitehead center group, Whitehead product. 
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     author = {Marek Golasi\'nski and Thiago de Melo},
     title = {Generalized {Gottlieb} and {Whitehead} center groups of space forms},
     journal = {Homology, homotopy, and applications},
     pages = {323--340},
     publisher = {mathdoc},
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     number = {1},
     year = {2019},
     doi = {10.4310/HHA.2019.v21.n1.a15},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a15/}
}
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Marek Golasiński; Thiago de Melo. Generalized Gottlieb and Whitehead center groups of space forms. Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 323-340. doi : 10.4310/HHA.2019.v21.n1.a15. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a15/

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