Finiteness conjecture for low-volume hyperbolic knot complements with hidden symmetries
Finiteness conjecture for low-volume hyperbolic knot complements with hidden symmetries
A hyperbolic knot complement is the complement of a knot in admitting a complete finite-volume hyperbolic structure, and its volume is denoted by . A knot complement has hidden symmetries when it non-normally covers another hyperbolic -manifold.
Finiteness conjecture. For any , at most finitely many hyperbolic knot complements have hidden symmetries and volume less than .
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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