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We construct a quantum Frobenius map for the   $SL_{3}$   skein module of any oriented 3-manifold specialized at a root of unity, and describe the map by way of threading certain polynomials along links. The homomorphism is a higher rank version of the Chebyshev–Frobenius homomorphism of Bonahon–Wong. The strategy builds on a previous construction of the Frobenius map for   $SL_{3}$   skein algebras of punctured surfaces, using the Frobenius map of Parshall–Wang for the quantum group   $\mathcal{O}_{q}(SL_{3}).$

Miraculous Cancellations and the Quantum Frobenius for SL 3 Skein Modules