Topological resolutions in K(2)-local homotopy theory at the prime 2

Irina Bobkova, Paul G. Goerss

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We provide a topological duality resolution for the spectrum E2 hs1/2, which itself can be used to build the K(2)-local sphere. The resolution is built from spectra of the form E2 hF where E2 is the Morava spectrum for the formal group of a supersingular curve at the prime 2 and F is a finite subgroup of the automorphisms of that formal group. The results are in complete analogy with the resolutions of Goerss, Henn, Mahowald and Rezk (Ann. of Math. (2) 162 (2005) 777–822) at the prime 3, but the methods are of necessity very different. As in the prime 3 case, the main difficulty is in identifying the top fiber; to do this, we make calculations using Henn's centralizer resolution.

Original languageEnglish (US)
Pages (from-to)917-956
Number of pages40
JournalJournal of Topology
Volume11
Issue number4
DOIs
StatePublished - Dec 2018

Keywords

  • 55P42
  • 55Q10
  • 55Q40
  • 55Q45 (primary)

ASJC Scopus subject areas

  • Geometry and Topology

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