2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224853The first part of this paper consists of lecture notes which summarize the machinery of filtered root invariants. A conceptual notion of "homotopy Greek letter element" is also introduced, and evidence is presented that it may be related to the root invariant. In the second part we compute some low dimensional root invariants of v_1-periodic elements at the prime 2.This is the version published by Geometry & Topology Monographs on 29 January 2007Algebraic Topology55Q45, 55Q51, 55T15text