Geodesic
Splittings in the Burnside ring and in $SF_G$
Homology, homotopy, and applications, Tome 10 (2008) no. 1, pp. 1-27.

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

Let $G$ be a finite $p$-group, $p \neq 2$. We construct a map from the space $J_G$, defined as the fiber of $\psi^k-1: B_G O \to B_G Spin$, to the space $(SF_G)_p$, defined as the 1-component of the zeroth space of the equivariant $p$-complete sphere spectrum. Our map produces the same splitting of the $G$-connected cover of $(SF_G)_p$ as we have described in previous work, but it also induces a natural splitting of the $p$-completions of the component groups of fixed point subspaces.
DOI : 10.4310/HHA.2008.v10.n1.a1
Classification : 19L20, 19L47, 55R91
Keywords: $J$-homomorphism, Burnside ring, sphere spectru 
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     title = {Splittings in the {Burnside} ring and in $SF_G$},
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     pages = {1--27},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n1.a1/}
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Christopher P. French. Splittings in the Burnside ring and in $SF_G$. Homology, homotopy, and applications, Tome 10 (2008) no. 1, pp. 1-27. doi : 10.4310/HHA.2008.v10.n1.a1. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n1.a1/

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