A log PSS morphism with applications to Lagrangian embeddings

Let $M$ be a smooth projective variety and $\mathbf{D}$ an ample normal crossings divisor. From topological data associated to the pair $(M, \mathbf{D})$, we construct, under assumptions on Gromov-Witten invariants, series of distinguished classes in symplectic cohomology complement $X = M \backslash \mathbf{D}$. Under further "topological" pair, these can organized into Log(arithmic) PSS morphism, from vector space which term logarithmic \mathbf{D})$ cohomology. Turning applications, show that methods some knowledge invariants used produce dilations quasi-dilations (in sense Seidel-Solomon [SS]) examples such as conic bundles. In turn, existence elements imposes strong restrictions exact Lagrangian embeddings, especially dimension 3. For instance, prove any complex 3-dimensional bundle over $(\mathbb{C}^*)^2$ must diffeomorphic $T^3$ or connect sum $\#^n S^1 \times S^2$.