Nonhyperbolic Dehn fillings on hyperbolic 3-manifolds

Mario Eudave-Muñoz and Ying-Qing Wu

Vol. 190 (1999), No. 2, 261–275

DOI: 10.2140/pjm.1999.190.261

Abstract

In this paper we will give three infinite families of examples of nonhyperbolic Dehn fillings on hyperbolic manifolds. A manifold in the first family admits two Dehn fillings of distance two apart, one of which is toroidal and annular, and the other is reducible and ∂-reducible. A manifold in the second family has boundary consisting of two tori, and admits two reducible Dehn fillings. A manifold in the third family admits a toroidal filling and a reducible filling with distance 3 apart. These examples establish the virtual bounds for distances between certain types of nonhyperbolic Dehn fillings.

Milestones

Received: 15 September 1997

Revised: 2 February 1998

Published: 1 October 1999