On hyperbolic knots in S-3 with exceptional surgeries at maximal distance

Benjamin Audoux (1) , Ana G Lecuona (1) , Fionntan Roukema (2)

1 I2M - Institut de Mathématiques de Marseille
2 SoMaS - School of Mathematics and Statistics [Sheffield]

Baker showed that 10 of the 12 classes of Berge knots are obtained by surgery on the minimally twisted 5-chain link. In this article we enumerate all hyperbolic knots in S 3 obtained by surgery on the minimally twisted 5-chain link that realise the maximal known distances between slopes corresponding to exceptional (lens, lens), (lens, toroidal), (lens, Seifert fibred spaces) pairs. In light of Baker's work, the classification in this paper conjecturally accounts for " most" hyper-bolic knots in S 3 realising the maximal distance between these exceptional pairs. All examples obtained in our classification are realised by filling the magic manifold. The classification highlights additional examples not mentioned in Martelli and Petronio's survey of the exceptional fillings on the magic manifold. Of particular interest, is an example of a knot with two lens space surgeries that is not obtained by filling the Berge manifold.

Mots clés: Berge manifold; 3-manifolds; maximal distance; exceptional surgeries; hyperbolic knot; 5-chain link; Dehn surgery; Martelli and Petronio's survey; magic manifold; lens space surgeries

Domaines: Topologie géométrique [math.GT]

Benjamin Audoux, Ana G Lecuona, Fionntan Roukema. On hyperbolic knots in S-3 with exceptional surgeries at maximal distance. Algebraic and Geometric Topology, 2018, 18 (4), pp.2371-2417. ⟨10.2140/agt.2018.18.2371⟩. ⟨hal-01485358⟩