2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72901A formula for the Arf invariant of a link is given in terms of the singularities of an immersed surface bounded by the link. This is applied to study the computational complexity of quantum invariants of 3--manifolds.Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper9.abs.htmlGeometric TopologyAlgebraic Topology57M27, 68Q15text