The homotopy of the K(2)-local Moore spectrum at the prime 3 revisited

2008/11/03 by Hans-Werner Henn, Henn, Hans-Werner, Nasko Karamanov +3
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #math.AT

paper · pdf · doi:10.48550/arxiv.0811.0235

40 pages

arxiv created 2008/11/03 · arxiv updated 2009/12/01

Abstract

In this paper we use the approach introduced in an earlier paper by Goerss, Henn, Mahowald and Rezk in order to analyze the homotopy groups of L_K(2)V(0), the mod-3 Moore spectrum V(0) localized with respect to Morava K-theory K(2). These homotopy groups have already been calculated by Shimomura. The results are very complicated so that an independent verification via an alternative approach is of interest. In fact, we end up with a result which is more precise and also differs in some of its details from that of Shimomura. An additional bonus of our approach is that it breaks up the result into smaller and more digestible chunks which are related to the K(2)-localization of the spectrum TMF of topological modular forms and related spectra. Even more, the Adams-Novikov differentials for L_K(2)V(0) can be read off from those for TMF.

Related

• The homotopy groups of the spectrum Tmf
• The Adams spectral sequence for 3-local tmf
• The Omega spectrum for mod 2 KO-theory
• On the Bousfield-Kan spectral sequence for Q(2)₍₃₎
• Denominators of special values of zeta-functions count KU-local homotopy groups of mod p Moore spectra