Nonhyperbolic Dehn fillings on hyperbolic 3-manifolds

Details Nonhyperbolic Dehn fillings on hyperbolic 3-manifolds Nonhyperbolic Dehn fillings on hyperbolic 3-manifolds

1997-08-07

arxiv.org/abs/math/9708206v1

Mathematics

Geometric Topology

Scientific paper

We 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 $\partial$-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.

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