Finiteness conjecture for low-volume hyperbolic knot complements with hidden symmetries

A hyperbolic knot complement is the complement of a knot in S3S^3 admitting a complete finite-volume hyperbolic structure, and its volume is denoted by volM\operatorname{vol} M. A knot complement has hidden symmetries when it non-normally covers another hyperbolic 33-manifold.

Finiteness conjecture. For any R>0R>0, at most finitely many hyperbolic knot complements have hidden symmetries and volume less than RR.

The conjecture is motivated by results producing infinite families of non-accidental-parabolic hyperbolic knot complements without hidden symmetries, while hidden symmetries are known to be rare among knot complements. Its resolution is not stated in the supplied source.

Sources & referencesView supporting material

Primary source

Eric Chesebro, Jason DeBlois and Priyadip Mondal, “Generic hyperbolic knot complements without hidden symmetries”, arXiv:1910.04712 (2019).

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