A resolution of the K(2)-local sphere at the prime 3

• Autores: P. Goerss, Hans-Werner Henn, Misha A. Mahowald, C. Rezk
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 162, Nº 2, 2005, págs. 777-822
• Idioma: inglés
• DOI: 10.4007/annals.2005.162.777
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• Resumen

  • We develop a framework for displaying the stable homotopy theory of the sphere, at least after localization at the second Morava K-theory K(2). At the prime 3, we write the spectrum LK(2)S0 as the inverse limit of a tower of fibrations with four layers. The successive fibers are of the form EhF 2 where F is a finite subgroup of the Morava stabilizer group and E2 is the second Morava or Lubin-Tate homology theory. We give explicit calculation of the homotopy groups of these fibers. The case n = 2 at p = 3 represents the edge of our current knowledge: n = 1 is classical and at n = 2, the prime 3 is the largest prime where the Morava stabilizer group has a p-torsion subgroup, so that the homotopy theory is not entirely algebraic.