The Borman–Sheridan class compatibility conjecture

Let $\pi:X\to Y$ be a rank-one algebraic torus fibration degenerating over a divisor $D\subset Y$, and let $\tau\in SH^2(Y\setminus D)$ be the class corresponding to a simple Reeb orbit going once around $D$. The categories $\mathcal{W}_{S^1}(X)_{-1}$ and $\mathcal{W}(Y\setminus D)$ are related by the conjectural equivalence

$$\mathcal{W}_{S^1}(X)_{-1}\cong\mathcal{W}(Y\setminus D).$$

Borman–Sheridan class compatibility conjecture. Under this equivalence, the action of $t$ on $\mathcal{W}_{S^1}(X)_{-1}$ coincides with the action of $\tau$ on $\mathcal{W}(Y\setminus D)$. This specifies the additional $\mathbb{C}[t]$-linear structure expected on the category of the complement of the discriminant divisor.