On the existence of a v_2^32-self map on M(1,4) at the prime 2

TL;DR

This paper proves the existence of a specific v_2^32-self map on M(1,4) at the prime 2, which leads to new periodic families in the stable homotopy groups of spheres.

Contribution

It establishes the existence of a minimal v_2-self map on M(1,4), extending known self-maps and revealing new periodic phenomena in stable homotopy groups.

Findings

Existence of v_2^32-self map on M(1,4) at prime 2

Implication of 192-periodic families in stable homotopy groups

Extension of known self-maps to higher chromatic levels

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_1^4: Sigma^8 M(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 v_2^32: Sigma^192 M(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.