The wrapped microlocal sheaves conjecture for Weinstein manifolds

Let $W$ be a Weinstein manifold, or a Weinstein pair, with skeleton

$$. **Wrapped microlocal sheaves conjecture.** There is a cosheaf of$$

-dg categories, denoted by

$$, on$$

such that

$$\simeq \operatorname{Fuk}^{wr}(W).$$

If $W$ is a Weinstein pair, this is the partially wrapped category, with stops determined by $\Sigma$. If $W\cong T^*X$ with its standard cotangent Liouville structure, possibly also with Weinstein pair structure, and $\Lambda$ denotes the skeleton of $T^*X$, then on $\Lambda\cong$ there is an equivalence of cosheaves

$$\cong (\mu\operatorname{Sh}^{wr}_{\Lambda})_{\mathbf{Z}/2}.$$

This conjecture proposes a sheaf-theoretic model for wrapped Fukaya categories and, in the cotangent-bundle case, identifies it with the previously defined wrapped microlocal-sheaf cosheaf. It is presented as an elaboration of Kontsevich's original conjecture; the supplied text gives no resolution status.