On the Thom spectra over Ω(𝑆𝑈(𝑛)/𝑆𝑂(𝑛)) and Mahowald’s 𝑋_{𝑘} spectra

Yan, Dung Yung

doi:10.1090/S0002-9939-1992-1123672-0

On the Thom spectra over $\Omega (\textrm {SU}(n)/\textrm {SO}(n))$ and Mahowald’s $X_ k$ spectra
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Proc. Amer. Math. Soc. 116 (1992), 567-573 Request permission

Abstract:

The Thom spectra $M(n)\quad ({2^k} \leq n \leq {2^{k + 1}} - 1)$ induced from $\Omega (\operatorname {SU}(n)/\operatorname {SO}(n)) \to BO$ is a wedge of suspensions of Mahowald’s ${X_k}$ spectra that is induced from $\Omega {J_{{2^k} - 1}}{S^2} \to {\Omega ^2}{S^3} \to BO$, where ${J_i}$ is the $i$th stage of the James construction.

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