The Modulo Two Homotopy Groups of the 𝐿₂-Localization of the Ravenel Spectrum

  • Ippei Ichigi Department of Mathematics, Faculty of Science, Kochi University, Kochi, 780-8520, Japan.
  • Katsumi Shimomura Department of Mathematics, Faculty of Science, Kochi University, Kochi, 780-8520, Japan.
Keywords: homotopy groups, Bousfield-Ravenel localization, Ravenel spectrum

Abstract

The Ravenel spectra T(m) for non-negative integers m interpolate between the sphere spectrum and the Brown-Peterson spectrum. Let L2 denote the Bousfield-Ravenel localization functor with respect to v2−1BP. In this paper, we determine the homotopy groups π(L2T(m) : ℤ/2) = [M2, L2T(m)] for m > 1, where M2 denotes the modulo two Moore spectrum.

Published
2008-10-01
How to Cite
[1]
I. Ichigi and K. Shimomura, “The Modulo Two Homotopy Groups of the 𝐿₂-Localization of the Ravenel Spectrum”, CUBO, vol. 10, no. 3, pp. 43–55, Oct. 2008.