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

M. Behrens, M. Hill, M.J. Hopkins and M. Mahowald

Let M(1) be the mod 2 Moore spectrum. J.F. Adams proved that M(1) admits a minimal v₁-self map v₁⁴: Σ⁸ 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: 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.

Homology, Homotopy and Applications, Vol. 10 (2008), No. 3, pp.45-84.

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