Embedding Fukaya category into the equivariant Tamarkin (sheaf) category

Establish the existence of an infinitesimally wrapped Fukaya category Fuk(T^*M) for nonexact Lagrangian submanifolds in the cotangent bundle T^*M and construct a natural embedding functor from Fuk(T^*M) into the equivariant Tamarkin sheaf category Sh_{τ>0}^{R^δ}(M×R_t).

Background

The paper develops spectral networks (Stokes graphs) for higher-order differentials under the strongly GMN condition and uses wall-crossing data to build sheaf quantizations. In this framework, the equivariant Tamarkin category Sh_{τ>0}^{R^δ}(M×R_t) serves as a sheaf-theoretic model for quantizations that should mirror objects of an infinitesimally wrapped Fukaya category of nonexact Lagrangians.

The conjecture posits a foundational link between symplectic geometry and sheaf theory: that a Fukaya-type category for nonexact Lagrangians in T^*M not only exists but embeds into Sh_{τ>0}^{R^δ}(M×R_t). The authors note that this conjecture has been checked for integral Lagrangians in KPS, indicating partial progress but leaving the general case open.