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July, 2003 Dehn Filling of Cusped Hyperbolic 3-Manifolds with Geodesic Boundary
Roberto Frigerio, Bruno Martelli, Carlo Petronio
J. Differential Geom. 64(3): 425-455 (July, 2003). DOI: 10.4310/jdg/1090427000


We define for each $g \geq 2$ and $k \geq 0$ a set $\mathcal{M}_{g,k}$ of orientable hyperbolic 3-manifolds with $k$ toric cusps and a connected totally geodesic boundary of genus $g$. Manifolds in $\mathcal{M}_{g,k}$ 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 $\mathcal{M}_{g,k}$ for a fixed $k$ has growth type $g^g$.

We completely describe the non-hyperbolic Dehn fillings of each $M$ in $\mathcal{M}_{g,k}$, 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 $\partial$-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 $\partial$-reducible fillings are handlebodies.


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Roberto Frigerio. Bruno Martelli. Carlo Petronio. "Dehn Filling of Cusped Hyperbolic 3-Manifolds with Geodesic Boundary." J. Differential Geom. 64 (3) 425 - 455, July, 2003.


Published: July, 2003
First available in Project Euclid: 21 July 2004

zbMATH: 1073.57010
MathSciNet: MR2032111
Digital Object Identifier: 10.4310/jdg/1090427000

Rights: Copyright © 2003 Lehigh University


Vol.64 • No. 3 • July, 2003
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