On the existence of a v₂³2-self map on M(1,4) at the prime 2

2007/10/29 by Mark Behrens, Michael A. Hill, Behrens, Mark +5 · 2 citations
Mathematics · #55Q40 #55Q51 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0710.5426

openalex publication_date 2007/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M(1) be the mod 2 Moore spectrum. J.F. Adams proved that M(1) admits a minimal v₁-self map v₁⁴: Sigma⁸ 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 v₂-self map of the form v₂³2: Sigma¹92 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.

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