2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222732We prove the hyperbolization theorem for punctured torus bundles and two-bridge link complements by decomposing them into ideal tetrahedra which are then given hyperbolic structures, following Rivin's volume maximization principle.This is the version published by Geometry & Topology on 16 September 2006. Appendix by David FuterGeometric Topology57M50, 57M27On canonical triangulations of once-punctured torus bundles and two-bridge link complementstext