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Pré-Publication, Document De Travail Année : 2016

Knot complements, hidden symmetries and reflection orbifolds

Résumé

In this article we examine the conjecture of Neumann and Reid that the only hyperbolic knots in the $3$-sphere which admit hidden symmetries are the figure-eight knot and the two dodecahedral knots. Knots whose complements cover hyperbolic reflection orbifolds admit hidden symmetries, and we verify the Neumann-Reid conjecture for knots which cover small hyperbolic reflection orbifolds. We also show that a reflection orbifold covered by the complement of an AP knot is necessarily small. Thus when $K$ is an AP knot, the complement of $K$ covers a reflection orbifold exactly when $K$ is either the figure-eight knot or one of the dodecahedral knots.

Dates et versions

hal-01302551 , version 1 (14-04-2016)

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Michel Boileau, Steven Boyer, Radu Cebanu, Genevieve S. Walsh. Knot complements, hidden symmetries and reflection orbifolds. 2016. ⟨hal-01302551⟩
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