2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66825Let V(1) be the Smith-Toda complex at the prime 3. We prove that there exists a map v_2^9: Σ^{144}V(1) \to V(1) that is a K(2) equivalence. This map is used to construct various v_2-periodic infinite families in the 3-primary stable homotopy groups of spheres.41 pages, 6 figures, submitted to proceedings of the Northwestern University conference on algebraic topology, March 2002Algebraic Topology55Q51; 55Q45, 55T15text