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

Behrens, Mark; Hill, Michael; Hopkins, Michael J.; Mahowald, Mark

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

Authors

Description

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.
31 pages, 16 figures. Revised version: includes new section (section 9)explaining centrality of d_2(v_2^8) and d_3(v_2^16), and fixes an error in section 7