Gunningham–Safronov's generic skein–DT sheaf conjecture

Let qq be generic, let MM be a connected closed oriented 3-manifold, let RG(M)R_G(M) be its representation variety, and let ϕRG(M)\phi_{R_G(M)} denote the DT sheaf on it. Let SkG(M)\mathrm{Sk}_G(M) be the GG-skein module.

Skein–DT sheaf conjecture. There is an isomorphism

SkG(M)H0(RG(M),ϕRG(M)).\mathrm{Sk}_G(M)\cong \mathrm{H}^0(R_G(M),\phi_{R_G(M)}).

The right-hand side is sheaf-theoretic framed instanton Floer homology, introduced by Abouzaid and Manolescu, and the conjecture relates generic skein modules to cohomological Donaldson–Thomas theory. The source does not state whether the conjecture has been resolved.

Sources & referencesView supporting material

Primary source

Chun-Yu Bai, “Derived skein module”, arXiv:2606.11122 (2026).

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