Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 115-118). / 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. / by Umut Varolgunes. / Ph. D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/117315 |
| Date | January 2018 |
| Creators | Varolgunes, Umut |
| Contributors | Paul Seidel., Massachusetts Institute of Technology. Department of Mathematics., Massachusetts Institute of Technology. Department of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 118 pages, application/pdf |
| Rights | MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission., http://dspace.mit.edu/handle/1721.1/7582 |
Page generated in 0.3133 seconds