Geometry & Topology Monographs 10 (2007) 319–332

DOI: 10.2140/gtm.2007.10.319

arXiv: 0903.4662

Abstract

Let E(n) and T(m) for nonnegative integers n and m denote the Johnson--Wilson and the Ravenel spectra, respectively. Given a spectrum whose E(n)_*–homology is E(n)_*(T(m))/(v₁,…,v_n-1), then each homotopy group of it estimates the order of each homotopy group of L_nT(m). We here study the E(n)–based Adams E₂–term of it and present that the determination of the E₂–term is unexpectedly complex for odd prime case. At the prime two, we determine the E_∞–term for π_*(L₂T(1)/(v₁)), whose computation is easier than that of π_*(L₂T(1)) as we expect.

Keywords

Ravenel spectrum, Bousfield localization, Johnson–Wilson spectrum, Adams–Novikov spectral sequence

Mathematical Subject Classification

Primary: 55Q99

References

Publication

Received: 31 August 2004
Revised: 16 September 2005
Published: 18 April 2007

Authors