The Solomon–Verbitsky Fukaya/deformation-quantisation quasi-isomorphism conjecture

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Let L\mathfrak{L} be a Solomon–Verbitsky collection of Lagrangian submanifolds in a holomorphic symplectic manifold (X,σ)(\mathrm{X},\sigma). Let A^L\widehat{\mathcal{A}}_\mathfrak{L} be the local Fukaya category and let DQLs\mathcal{DQ}^{\mathrm{s}}_\mathfrak{L} be the full differential graded subcategory containing one chosen quantised orientation for each Lagrangian. Solomon–Verbitsky correspondence conjecture. There is a quasi-isomorphism

A^L≅IndNov/C((ℏ))(DQLs).\widehat{\mathcal{A}}_\mathfrak{L}\cong \mathrm{Ind}_{\mathrm{Nov}/\mathbf{C}((\hbar))}\left(\mathcal{DQ}^{\mathrm{s}}_\mathfrak{L}\right).

This is proposed as a local form of the generalised Riemann–Hilbert correspondence and as a comparison between the Fukaya and de Rham models; it is not proved in the source.

References

Primary source

Borislav Mladenov, “Differential graded categories in holomorphic symplectic geometry”, arXiv:2604.06630 (2026).

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