Morava E-homology of Bousfield-Kuhn functors on odd-dimensional spheres

TL;DR

This paper provides explicit descriptions of the completed E-homology of Bousfield-Kuhn functors on odd-dimensional spheres at chromatic level 2, extending previous results at level 1 and connecting to K-theory localizations.

Contribution

It introduces explicit presentations for the E-homology of Bousfield-Kuhn functors at chromatic level 2, building on Behrens and Rezk's spectral algebra model.

Findings

Explicit E-homology presentations at chromatic level 2

Comparison with level 1 case and K-theory localizations

Enhanced understanding of unstable v_n-periodic homotopy theory

Abstract

As an application of Behrens and Rezk's spectral algebra model for unstable v_n-periodic homotopy theory, we give explicit presentations for the completed E-homology of the Bousfield-Kuhn functor on odd-dimensional spheres at chromatic level 2, and compare them to the level 1 case. The latter reflects earlier work in the literature on K-theory localizations.