The rational homotopy of the $K(2)$-local sphere and the chromatic splitting conjecture for the prime 3 and level 2

Paul G. Goerss; Hans-Werner Henn; Mark Mahowald

doi:10.4171/dm/480

JournalsdmVol. 19pp. 1271–1290

The rational homotopy of the $K (2)$ -local sphere and the chromatic splitting conjecture for the prime 3 and level 2

Paul G. Goerss
Hans-Werner Henn
Mark Mahowald

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Abstract

We calculate the rational homotopy of the $K (2)$ -local sphere $L_{K (2)} S^{0}$ at the prime 3 and confirm Hopkins' chromatic splitting conjecture for $p = 3$ and $n = 2$ .

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Paul G. Goerss, Hans-Werner Henn, Mark Mahowald, The rational homotopy of the $K (2)$ -local sphere and the chromatic splitting conjecture for the prime 3 and level 2. Doc. Math. 19 (2014), pp. 1271–1290

DOI 10.4171/DM/480