Geodesic
The second real Johnson-Wilson theory and nonimmersions of $RP^n$
Homology, homotopy, and applications, Tome 10 (2008) no. 3, pp. 223-268.

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

Hu and Kriz construct the real Johnson-Wilson spectrum, $ER(n)$, which is $2^{n+2}(2^n-1)$-periodic, from the $2(2^n-1)$-periodic spectrum $E(n)$. $ER(1)$ is just $KO_{(2)}$ and $E(1)$ is just $KU_{(2)}$. We compute $ER(n)^*(RP^{\infty})$ and set up a Bockstein spectral sequence to compute $ER(n)^*(-)$ from $E(n)^*(-)$. We combine these to compute $ER(2)^*(RP^{2n})$ and use this to get new nonimmersions for real projective spaces. Our lowest dimensional new example is an improvement of 2 for $RP^{48}$.
DOI : 10.4310/HHA.2008.v10.n3.a11
Classification : 55N20, 55N91, 55T25, 57R42
Keywords: real projective space, nonimmersions, Johnson-Wilson theories 
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Nitu Kitchloo; W. Stephen Wilson. The second real Johnson-Wilson theory and nonimmersions of $RP^n$. Homology, homotopy, and applications, Tome 10 (2008) no. 3, pp. 223-268. doi : 10.4310/HHA.2008.v10.n3.a11. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n3.a11/

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