The Brown-Comenetz dual of the K(2)-local sphere at the prime 3

2012/12/12 by Paul G. Goerss, Goerss, Paul G., Hans-Werner Henn +1
Mathematics · #55Q45 #55Q51 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55Q45 #msc:55Q51

paper · pdf · doi:10.48550/arxiv.1212.2836

arxiv created 2014/05/07 · arxiv updated 2014/05/09

Abstract

We calculate the homotopy type of the Brown-Comenetz dual I₂ of the K(2)-local sphere at the prime 3 and show that there is a twisting by a non-trivial element P in the exotic part of the Picard group. We give a complete characterization of P as well. The main technique is to give a sequence of calculations of the homotopy groups of elements of the Picard group after smashing with the Smith-Toda complex V(1).

Related

• The Exotic K(2)-Local Picard Group at the Prime 2
• Bounding the K(p-1)-local exotic Picard group at p>3
• The rational homotopy of the K(2)-local sphere and the chromatic splitting conjecture for the prime 3 and level 2
• The α-Family in the K(2)-Local Sphere at the Prime 2
• On Hopkins' Picard group