The Vol-Det conjecture for alternating hyperbolic links

From papers

Let KK be an alternating hyperbolic link in S3S^3. Its hyperbolic volume is denoted by vol(K)=vol(S3K)\operatorname{vol}(K)=\operatorname{vol}(S^3\setminus K), and its determinant by det(K)\det(K). Vol-Det conjecture.

vol(K)<2πlogdet(K).\operatorname{vol}(K)<2\pi\log\det(K).

This conjecture relates two fundamental link invariants, hyperbolic volume and determinant, and was formulated by Champanerkar, Kofman, and Purcell. The supplied text does not indicate whether it has been resolved.

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Sources & referencesView supporting material

Primary source

Andrei Egorov and Andrei Vesnin, “The Vol-Det Conjecture for highly twisted alternating links”, arXiv:2411.11711 (2024).

Additional references

2 papers in this index state this conjecture (2018–2024). The statement above is taken from the most recent of them; the others are arXiv:1805.05490.

Solutions 0

No solutions have been posted yet.