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

• 成果类型: Article
• 署名作者: Goerss, P; Henn, HW; Mahowald, M; Rezk, C
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.162.777
• 发表日期: 2005
• 页码: 777-822
• 关键词: homotopy-groups; SUBGROUPS; MODULI; SPACE

摘要

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 L-K(2) S-0 as the inverse limit of a tower of fibrations with four layers. The successive fibers are of the form E-2(hF) where F is a finite subgroup of the Morava stabilizer group and E-2 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.