The alternating torus-knot 3D index conjecture
Let be coprime integers with , and let be a -efficient ideal triangulation of the complement of the torus knot. The alternating torus-knot 3D index conjecture. The index satisfies
This generalizes the computed trefoil case and was conjectured on physical grounds for alternating torus knots. The supplied source does not indicate whether the conjecture has been resolved.
References
Primary source
Daniele Celoria, Craig D. Hodgson and J. Hyam Rubinstein, “The 3D index and Dehn filling”, arXiv:2509.09886 (2025).
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