Existence of the Greek Letter Elements in the Stable Homotopy Groups of $E(n{)}_{\ast }$-Localized Spheres

Abstract

Let $E_2^{\ast .\ast }(X)$ denote the $E_2$-term of the Adams–Novikov spectral sequence converging to the homotopy groups of $X$. We can define the Greek letter elements in $E_2^{\ast .\ast }(L_n{S}^0)$ in the same way as those in $E_2^{\ast .\ast }(S^0)$. We show that these of $E_2^{\ast .\ast }(L_n{S}^0)$ are permanent cycles, though we know little for $E_2^{\ast .\ast }(S^0)$.