Examples of bireducible Dehn fillings

Abstract

If an irreducible manifold M admits two Dehn fillings along distinct slopes each filling resulting in a reducible manifold, then we call these bireducible Dehn fillings. The first example of bireducible Dehn fillings is due to Gordon and Litherland. More recently, Eudave-Munoz and Wu presented the first infinite family of manifolds which admit bireducible Dehn fillings. We present another infinite family of hyperbolic manifolds which admit bireducible Dehn fillings. The manifolds obtained by the fillings are always the connect sum of two lens spaces.