Spherical space forms and Dehn filling

THIS PAPER concerns those Dehn fillings on a torally bounded 3-manifold which yield manifolds with a finite fundamental group. The focus will be on those torally bounded 3-manifolds which either contain an essential torus, or whose interior admits a complete hyperbolic structure. While we give several general results, our sharpest theorems concern Dehn fillings on manifolds which contain an essential torus. One of these results is a sharp ''finite surgery theorem.'' The proof includes a characterization of the finite fillings on ''generalized'' iterated torus knots with a complete classification for the iterated torus knots in the 3-sphere. We also give a proof of the so-called ''2 pi'' theorem of Gromov and Thurston, and obtain an improvement (by a factor of two) in the original estimates of Thurston on the number of non-negatively-curved Dehn fillings on a torally bounded 3-manifold whose interior admits a complete hyperbolic structure. Copyright (C) 1996 Elsevier Science Ltd.