Dehn filling of cusped hyperbolic 3-manifolds with geodesic boundary

Details Dehn filling of cusped hyperbolic 3-manifolds with geodesic boundary Dehn filling of cusped hyperbolic 3-manifolds with geodesic boundary

2003-01-11

arxiv.org/abs/math/0301114v1

J. Differential Geom. 64 (2003) 425-455

Mathematics

Geometric Topology

28 pages, 16 figures

Scientific paper

We define for each g>=2 and k>=0 a set M_{g,k} of orientable hyperbolic 3-manifolds with $k$ toric cusps and a connected totally geodesic boundary of genus g. Manifolds in M_{g,k} have Matveev complexity g+k and Heegaard genus g+1, and their homology, volume, and Turaev-Viro invariants depend only on g and k. In addition, they do not contain closed essential surfaces. The cardinality of M_{g,k} for a fixed k has growth type g^g. We completely describe the non-hyperbolic Dehn fillings of each M in M_{g,k}, showing that, on any cusp of any hyperbolic manifold obtained by partially filling M, there are precisely 6 non-hyperbolic Dehn fillings: three contain essential discs, and the other three contain essential annuli. This gives an infinite class of large hyperbolic manifolds (in the sense of Wu) with boundary-reducible and annular Dehn fillings having distance 2, and allows us to prove that the corresponding upper bound found by Wu is sharp. If M has one cusp only, the three boundary-reducible fillings are handlebodies.

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