2024-03-132024-03-132022-08-12David Futer, Jessica S. Purcell, Saul Schleimer, Effective drilling and filling of tame hyperbolic 3-manifolds. Comment. Math. Helv. 97 (2022), no. 3, pp. 457–512. DOI 10.4171/CMH/5361420-8946http://hdl.handle.net/20.500.12613/9862We give effective bilipschitz bounds on the change in metric between thick parts of a cusped hyperbolic 3-manifold and its long Dehn fillings. In the thin parts of the manifold, we give effective bounds on the change in complex length of a short closed geodesic. These results quantify the filling theorem of Brock and Bromberg, and extend previous results of the authors from finite volume hyperbolic 3-manifolds to any tame hyperbolic 3-manifold. To prove the main results, we assemble tools from Kleinian group theory into a template for transferring theorems about finite-volume manifolds into theorems about infinite-volume manifolds.We also prove and apply an infinite-volume version of the 6-Theorem.56 pagesengAttribution CC BYhttps://creativecommons.org/licenses/by/4.0/Cone manifoldDehn fillingDehn surgeryMargulis numberHyperbolic manifoldText