  A complete embedding is a symplectic embedding $\iota:Y\to M$ of a
geometrically bounded symplectic manifold $Y$ into another geometrically
bounded symplectic manifold $M$ of the same dimension. When $Y$ satisfies an
additional finiteness hypothesis, we prove that the truncated relative
symplectic cohomology of a compact subset $K$ inside $Y$ is naturally
isomorphic to that of its image $\iota(K)$ inside $M$. Under the assumption
that the torsion exponents of $K$ 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.
