On the existence of a v_2^32self map on M(1,4) at the prime 2
Abstract
Let M(1) be the mod 2 Moore spectrum. J.F. Adams proved that M(1) admits a minimal v_1self map v_1^4: Sigma^8 M(1) > M(1). Let M(1,4) be the cofiber of this selfmap. The purpose of this paper is to prove that M(1,4) admits a minimal v_2self 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 192periodic families of elements in the stable homotopy groups of spheres.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.5426
 Bibcode:
 2007arXiv0710.5426B
 Keywords:

 Mathematics  Algebraic Topology;
 55Q51;
 55Q40
 EPrint:
 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