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

P. Goerss, H. W. Kenn, M. Mahowald, C. Rezk

Research output: Contribution to journalArticlepeer-review


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 E2hF 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.

Original languageEnglish (US)
Pages (from-to)777-822
Number of pages46
JournalAnnals of Mathematics
Issue number2
StatePublished - Sep 2005

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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