On the existence of a $v2^32$-self map on $M(1,4)$ at the prime 2

Abstract

Let $M(1)$ be the mod 2 Moore spectrum. J.F. Adams proved that $M(1)$ admits a minimal $v_1$-self map $v^4_1 : \Sigma^8 M (1) \to M (1)$. Let $M(1, 4)$ be the cofiber of this self-map. The purpose of this paper is to prove that $M(1, 4)$ admits a minimal $v_2$-self map of the form $v^{32}_2 : \Sigma^{192} M (1,4) \to M (1,4)$. The existence of this map implies the existence of many 192-periodic families of elements in the stable homotopy groups of spheres..