Mayer-Vietoris property for relative symplectic cohomology
Name
1045425399-MIT.pdf
Description
Full printable version
Size
7.7 MB
Format
Adobe PDF
Checksum (MD5)
70baa61dca7527fbd88545c173e2c430
Author(s)
Varolgunes, Umut
Advisor(s)
Paul Seidel.
Date Issued
2018
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, I construct and investigate the properties of a Floer theoretic invariant called relative symplectic cohomology. The construction is based on Hamiltonian Floer theory. It assigns a module over the Novikov ring to compact subsets of closed symplectic manifolds. I show the existence of restriction maps, and prove that they satisfy the Hamiltonian isotropy invariance property, discuss a Kunneth formula, and do some example computations. Relative symplectic cohomology is then used to establish a general criterion for displaceability of subsets. Finally, moving on to the main contribution of my thesis, I 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 co isotropic submanifolds. The proof uses a deformation argument in which the topological energy zero (i.e. constant) Floer solutions are the main actors.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 115-118).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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