The volume bound after augmentation of an alternating link

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Let KK be a hyperbolic alternating link, and let BB be an augmented unknot around any two parallel strands of KK. Augmentation volume conjecture.

vol⁡(K)<vol⁡(K∪B)≤2πlog⁡det⁡(K).\operatorname{vol}(K) < \operatorname{vol}(K\cup B) \leq 2\pi\log\det(K).

This conjecture would give an upper bound on the volume change caused by drilling out an augmented unknot. The source states that it follows from the Vol-Det conjecture and presents it as a new bound whose general validity remains open.

References

Primary source

Abhijit Champanerkar, Ilya Kofman and Matilde Lalín, “Mahler Measure and the Vol-Det Conjecture”, arXiv:1805.05490 (2018).

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