Open Access
2008 The second real Johnson-Wilson theory and nonimmersions of $RP^n$
Nitu Kitchloo, W. Stephen Wilson
Homology Homotopy Appl. 10(3): 223-268 (2008).


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 $RP^{48}$.


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Nitu Kitchloo. W. Stephen Wilson. "The second real Johnson-Wilson theory and nonimmersions of $RP^n$." Homology Homotopy Appl. 10 (3) 223 - 268, 2008.


Published: 2008
First available in Project Euclid: 1 September 2009

zbMATH: 1160.55002
MathSciNet: MR2475624

Primary: 55N20 , 55N91 , 55T25 , 57R42

Keywords: Johnson-Wilson theories , nonimmersions , Real projective space

Rights: Copyright © 2008 International Press of Boston

Vol.10 • No. 3 • 2008
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