Mayer-Vietoris property for relative symplectic cohomology [article]

Umut Varolgunes
2020 arXiv   pre-print
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
more » ... tions, 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.
arXiv:1806.00684v3 fatcat:prfdodpplfbfrnupkohdtk4phq