Title: A resolution of the K(2)-local sphere at the prime 3
Authors: Paul Goerss, Hans-Werner Henn,
Mark Mahowald and Charles Rezk
Northwestern University, Universit\'e Louis Pasteur et CNRS,
Northwestern University, University of Illinois Urbana, IL 61801
ABSTRACT 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.