REDUCING DEHN FILLINGS AND SMALL SURFACES

Abstract

In this paper we investigate the distances between Dehn fillings on a hyperbolic 3-manifold that yield 3-manifolds containing essential small surfaces including non-orientable surfaces. In particular, we study the situations where one filling creates an essential sphere or projective plane, and the other creates an essential sphere, projective plane, annulus, Möbius band, torus or Klein bottle, for all eleven pairs of such non-hyperbolic manifolds.