The A-polynomial realization conjecture for once-cusped hyperbolic three-manifolds

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Let MM be a complete finite-volume once-cusped hyperbolic three-manifold. An ideal triangulation of MM is a triangulation whose vertices lie at the cusp, and an ideal triangulation yields a factor of the AA-polynomial when the corresponding gluing-equation data realizes that factor. A-polynomial realization conjecture. There exists an ideal triangulation T\mathcal{T} of MM that yields all factors of the AA-polynomial. This is presented as a speculative future application, and no resolution is given in the source.

References

Primary source

Tejas Kalelkar, Saul Schleimer and Henry Segerman, “Connecting essential triangulations I: via 2-3 and 0-2 moves”, arXiv:2405.03539 (2024).

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