Conjecture relating trisection invariants to Kashaev's invariant

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For an integer ngeq2ngeq 2, let XX be a closed connected 44-manifold, let (A,B,C)(A,B,C) be the Hopf triplet specified by the construction in the source, let IA,B,C(X)I_{A,B,C}(X) be its trisection invariant, and let Kn(X)K_n(X) be Kashaev's invariant of XX.

Kashaev's invariant conjecture. The invariants satisfy

IA,B,C(X)=n1+χ(X)dotKn(X).I_{A,B,C}(X)=n^{1+\chi(X)}dot K_n(X).

This is Conjecture 4.3 of the cited work of Chaidez, Cotler and Cui. The supplied text does not provide evidence that it has been proved or disproved.

References

Primary source

Catherine Meusburger, Vincentas Mulevicius and Fiona Torzewska, “Categorical 4-manifold invariants from trisection diagrams”, arXiv:2511.19384 (2025).

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