A stable approach to an unstable homotopy spectral sequence.
New theory and new applications are presented for a spectral sequence of \textit{M. Bendersky} and \textit{R. D. Thompson} [Am. J. Math. 122, No.3, 599--635 (2000; Zbl 0963.55010)], which is a sequence of Bousfield-Kan type that may converge to the \(v_1\)-periodic homotopy of a space \(X\). The main theoretical result here states that for suitable \(X\) the \(E_2\)-term is given by Ext in the category of stable \(p\)-adic Adams modules of \(QK^1(X;{\mathbb{Z}}\hat{_p})/\mathit{im} (\psi^p)\). New convergence criteria for the spectral sequence are also obtained. As an application, complete calculations of the spectral sequence are given for the exceptional Lie groups \(G_2\) and \(F_4\) at the prime 2. The determination of the 2-primary \(v_1\)-periodic homotopy of \(F_4\) is a new result.
scientific article; zbMATH DE number 1956005
scientific article