We deﬁne for each g >= 2 and k >= 0 a set Mg,k of orientable hyperbolic 3-manifolds with k toric cusps and a connected totally geodesic boundary of genus g. Manifolds in Mg,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 Mg,k for a ﬁxed k has growth type g^g. We completely describe the non-hyperbolic Dehn ﬁllings of each M in Mg,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 ∂ -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 ∂ -reducible ﬁllings are handlebodies.
|Autori:||FRIGERIO R; MARTELLI B; PETRONIO C|
|Titolo:||Dehn filling of cusped hyperbolic 3-manifolds with geodesic boundary|
|Anno del prodotto:||2003|
|Digital Object Identifier (DOI):||https://doi.org/10.1007/s00147-003-0571-9|
|Appare nelle tipologie:||1.1 Articolo in rivista|