Characteristic Subsurfaces, Character Varieties and Dehn Filling

Steve Boyer, Marc Culler, Peter B. Shalen, Xingru Zhang

Published 2006-11-22Version 1

We give new bounds for the distance between two exceptional filling slopes for a 1-cusped hyperbolic 3-manifold in several different situations. The distance between a reducible slope and a slope that produces a manifold with finite fundamental group is at most 2. The distance between a reducible slope and one that produces a very small manifold is also at most 2. The distance between a reducible slope and one which produces a manifold with a pi_1 injective torus is at most 4. The methods used involve both characteristic submanifold theory and the theory of the PSL(2,C) character variety.