Volume monotonicity under crossing changes for alternating hyperbolic links

Let KK be an alternating hyperbolic knot or link, and let KK' 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.

Sources & referencesView supporting material

Primary source

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

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