Gunningham–Safronov's generic skein–DT sheaf conjecture
Let be generic, let be a connected closed oriented 3-manifold, let be its representation variety, and let denote the DT sheaf on it. Let be the -skein module.
Skein–DT sheaf conjecture. There is an isomorphism
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.
References
Primary source
Chun-Yu Bai, “Derived skein module”, arXiv:2606.11122 (2026).
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