Conjecture relating trisection invariants to Kashaev's invariant

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.

Sources & referencesView supporting material

Primary source

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

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