On the existence of a $v^{32}_2$-self map on $M(1,4)$ at the prime 2

  title={On the existence of a \$v^\{32\}\_2\$-self map on \$M(1,4)\$ at the prime 2},
  author={Mark Joseph Behrens and Michael A. Hill and Michael J. Hopkins and Mark E. Mahowald},
  journal={Homology, Homotopy and Applications},
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. 

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