2023/10/10 by Yoel Groman, Umut Varolgunes · 2 citations
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models
paper · pdf · doi:10.1112/s0010437x23007492
A complete embedding is a symplectic embedding ι :Y→ 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 ι (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.