Volume monotonicity under crossing changes for alternating hyperbolic links

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Let KK be an alternating hyperbolic knot or link, and let K′K' be obtained by changing any proper subset of crossings of KK.

Volume monotonicity conjecture.

vol⁡(K′)<vol⁡(K).\operatorname{vol}(K')<\operatorname{vol}(K).

This conjecture predicts that changing any proper subset of crossings strictly decreases hyperbolic volume. The source presents the claim as a broader conjecture of which the weaving-knot volume bound is a special case and test; its resolution is not indicated here.

References

Primary source

Abhijit Champanerkar, Ilya Kofman and Jessica S. Purcell, “Volume bounds for weaving knots”, arXiv:1506.04139 (2016).

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