2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165616Harer-Kas-Kirby conjectured that every handle decomposition of the elliptic surface E(1)_{2,3} requires both 1- and 3-handles. We prove that the elliptic surface E(n)_{p,q} has a handle decomposition without 1-handles for $n\geq 1$ and (p,q)=(2,3),(2,5),(3,4),(4,5).23 pages, 56 figures, slightly extended, accepted for publication in J. TopolGeometric Topology57R55; 57R65; 57N13text