Minimum-volume conjecture for spherical knotoids

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A spherical knotoid is a knotoid in S2S^2 whose associated hyperbolic complement has a hyperbolic volume. The knotoid 212_1 denotes the spherical knotoid with the indicated two-crossing label.

Minimum-volume conjecture. The unique spherical knotoid of smallest volume is the knotoid 212_1, and its volume is approximately 5.33349…5.33349\dots.

This conjecture identifies the smallest-volume spherical knotoid and gives a numerical estimate for its volume. The supplied text does not state whether the claim has been proved or disproved.

References

Primary source

Colin Adams, Alexandra Bonat, Maya Chande, Joye Chen, Maxwell Jiang, Zachary Romrell, Daniel Santiago, Benjamin Shapiro and Dora Woodruff, “Hyperbolic Knotoids”, arXiv:2209.04556 (2022).

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