The Brown-Peterson homology of Mahowald’s 𝑋_{𝑘} spectra

Yan, Dung Yung

doi:10.1090/S0002-9947-1994-1272464-7

The Brown-Peterson homology of Mahowald’s $X_ k$ spectra
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Trans. Amer. Math. Soc. 344 (1994), 261-289 Request permission

Abstract:

We compute the Brown-Peterson homology of Mahowald’s ${X_k}$ spectrum which is the Thom spectrum induced from $\Omega {J_{{2^k} - 1}}{S^2} \to {\Omega ^2}{S^3} - {\text {BO}}$, and the edge homomorphism of the Adams-Novikov spectral sequence for ${\pi _\ast }({X_k})$. We then compute the nonnilpotent elements of ${\pi _\ast }({X_k})$.

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