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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 –parameter family of rank coisotropic submanifolds. The proof uses a deformation argument in which the topological energy zero (ie constant) Floer solutions are the main actors.
Varolgunes, Umut 1
@article{GT_2021_25_2_a0,
author = {Varolgunes, Umut},
title = {Mayer{\textendash}Vietoris property for relative symplectic cohomology},
journal = {Geometry & topology},
pages = {547--642},
publisher = {mathdoc},
volume = {25},
number = {2},
year = {2021},
doi = {10.2140/gt.2021.25.547},
url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2021.25.547/}
}
Varolgunes, Umut. Mayer–Vietoris property for relative symplectic cohomology. Geometry & topology, Tome 25 (2021) no. 2, pp. 547-642. doi : 10.2140/gt.2021.25.547. http://geodesic.mathdoc.fr/articles/10.2140/gt.2021.25.547/
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