2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64022We prove the existence of pure braids with arbitrarily many strands which are small, i.e. they contain no closed incompressible surface in the complement which is not boundary parallel. This implies the existence of irreducible non-Haken 3-manifolds of arbitrarily high Heegaard genus.10 pages, 12 figuresGeometric Topology57M50text