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The Adams-Novikov spectral sequence for the \(L_ 2\) localization of a \(v_ 2\) spectrum. (English) Zbl 0791.55005

Tangora, Martin C. (ed.), Algebraic topology, Oaxtepec 1991. Proceedings of an international conference on algebraic topology, held July 4-11, 1991 in Oaxtepec, Mexico. Providence, RI: American Mathematical Society. Contemp. Math. 146, 237-250 (1993).
Let \(X_ 1\) denote the Thom spectrum of the map \(\Omega S^ 2 \to BO\). Let \(D\) denote the cofiber of the map \(v_ 1: \Sigma^ 2 X_ 1 \to X_ 1\). In this paper the homotopy groups of the Bousfield localization \(L_{K(2)}D\) are computed. The method is to calculate the Adams-Novikov spectral sequence, which has many nontrivial \(d_ 3\)-differentials. The result of this calculation is expected to be useful in determining the \(v_ 2\)-periodic stable homotopy groups of spheres.
For the entire collection see [Zbl 0780.00041].

MSC:

55P42 Stable homotopy theory, spectra
55T15 Adams spectral sequences
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