Locality of relative symplectic cohomology for complete embeddings

A complete embedding is a symplectic embedding of a geometrically bounded symplectic manifold into another geometrically bounded symplectic manifold of the same dimension. When satisfies an additional finiteness hypothesis, we prove that the truncated relative symplectic cohomology of a compact subset inside is naturally isomorphic to that of its image inside. Under the assumption that the torsion exponents of are bounded, we deduce the same result for relative symplectic cohomology. We introduce a technique for constructing complete embeddings using what we refer to as integrable anti-surgery. We apply these to study symplectic topology and mirror symmetry of symplectic cluster manifolds and other examples of symplectic manifolds with singular Lagrangian torus fibrations satisfying certain completeness conditions.