We derive constraints on Lagrangian embeddings in completions of certain stable symplectic fillings whose symplectic cohomologies are semisimple. Manifolds with these properties can be constructed by generalizing the boundary connected sum operation to our setting, and are related to birational surgeries like blow-downs and flips. As a consequence, there are many nontoric (noncompact) monotone symplectic manifolds whose wrapped Fukaya categories are proper.
"Disjoinable Lagrangian tori and semisimple symplectic cohomology." Algebr. Geom. Topol. 20 (5) 2269 - 2335, 2020. https://doi.org/10.2140/agt.2020.20.2269