On the existence of a v232-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 v1-self map v14: Σ 8M(1) → 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 v232: Σ192M(1,4) → 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. Copyright © 2008, International Press.