#### Volume 25, issue 2 (2021)

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Mayer–Vietoris property for relative symplectic cohomology

### Umut Varolgunes

Geometry & Topology 25 (2021) 547–642
##### Abstract

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 natural geometric conditions in which relative symplectic cohomology of two subsets satisfies the Mayer–Vietoris property. These conditions involve certain integrability assumptions involving geometric objects called barriers — roughly, a $1$–parameter family of rank $2$ coisotropic submanifolds. The proof uses a deformation argument in which the topological energy zero (ie constant) Floer solutions are the main actors.

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##### Keywords
Floer theory, involutive systems, descent
##### Mathematical Subject Classification 2010
Primary: 53D40
Secondary: 53D37, 81S10