Dehn filling of the "magic" 3-manifold

Details Dehn filling of the "magic" 3-manifold Dehn filling of the "magic" 3-manifold

2002-04-18

arxiv.org/abs/math/0204228v3

Comm. Anal. Geom. 14 (2006), 967-1024

Mathematics

Geometric Topology

56 pages, 10 figures, 16 tables. Some consequences of the classification added

Scientific paper

We classify all the non-hyperbolic Dehn fillings of the complement of the chain-link with 3 components, conjectured to be the smallest hyperbolic 3-manifold with 3 cusps. We deduce the classification of all non-hyperbolic Dehn fillings of infinitely many 1-cusped and 2-cusped hyperbolic manifolds, including most of those with smallest known volume. Among other consequences of this classification, we mention the following: - for every integer n we can prove that there are infinitely many hyperbolic knots in the 3-sphere having exceptional surgeries n, n+1, n+2, n+3, with n+1, n+2 giving small Seifert manifolds and n, n+3 giving toroidal manifolds; - we exhibit a 2-cusped hyperbolic manifold that contains a pair of inequivalent knots having homeomorphic complements; - we exhibit a chiral 3-manifold containing a pair of inequivalent hyperbolic knots with orientation-preservingly homeomorphic complements; - we give explicit lower bounds for the maximal distance between small Seifert fillings and any other kind of exceptional filling.

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