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The second real Johnson-Wilson theory and non-immersions

By Nitu Kitchloo, W. Stephen Wilson and Communicated Donald M. Davis


Hu and Kriz construct the real Johnson-Wilson spectrum, ER(n), which is 2n+2 (2n − 1)-periodic, from the 2(2n − 1)periodic spectrum E(n). ER(1) is just KO (2) and E(1) is just KU (2). We compute ER(n) ∗ (RP ∞ ) 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. 1

Year: 2010
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