2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71769We prove that the three-sphere recognition problem lies in the complexity class NP. Our work relies on Thompson's original proof that the problem is decidable [Math. Res. Let., 1994], Casson's version of her algorithm, and recent results of Agol, Hass, and Thurston [ArXiv, 2002].36 pages, 12 figuresGeometric Topology57M40text