Mayer-Vietoris property for relative symplectic cohomology

Abstract

In this paper, we construct a Hamiltonian Floer theory based invariant called relative symplectic cohomology, which assigns a module over the Novikov ring to compact subsets of closed symplectic manifolds. We show the existence of restriction maps, and prove some basic properties. Our main contribution is to identify a natural geometric situation in which relative symplectic cohomology of two subsets satisfy the Mayer-Vietoris property. This is tailored to work under certain integrability assumptions, the weakest of which introduces a new geometric object called a barrier - roughly, a one parameter family of rank 2 coisotropic submanifolds. The proof uses a deformation argument in which the topological energy zero (i.e. constant) Floer solutions are the main actors.

v3. Final version, accepted for publication at Geometry & Topology

References in corpus (2)

• Covariantly functorial wrapped Floer theory on Liouville sectors
• Rabinowitz Floer homology and mirror symmetry

Cited by in corpus (4)

• Floer theory of disjointly supported Hamiltonians on symplectically aspherical manifolds
• Selective symplectic homology with applications to contact non-squeezing
• A characterization of heaviness in terms of relative symplectic cohomology
• Realizability in tropical geometry and unobstructedness of Lagrangian submanifolds