Mayer-Vietoris property for relative symplectic cohomology
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
| Published: |
Massachusetts Institute of Technology
2018
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/117315 |
| _version_ | 1826209851979595776 |
|---|---|
| author | Varolgunes, Umut |
| author2 | Paul Seidel. |
| author_facet | Paul Seidel. Varolgunes, Umut |
| author_sort | Varolgunes, Umut |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018. |
| first_indexed | 2024-09-23T14:32:49Z |
| format | Thesis |
| id | mit-1721.1/117315 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:32:49Z |
| publishDate | 2018 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1173152019-04-12T17:11:00Z Mayer-Vietoris property for relative symplectic cohomology Varolgunes, Umut Paul Seidel. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. 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. 2018-08-08T19:48:57Z 2018-08-08T19:48:57Z 2018 2018 Thesis http://hdl.handle.net/1721.1/117315 1045425399 eng 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 118 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Varolgunes, Umut Mayer-Vietoris property for relative symplectic cohomology |
| title | Mayer-Vietoris property for relative symplectic cohomology |
| title_full | Mayer-Vietoris property for relative symplectic cohomology |
| title_fullStr | Mayer-Vietoris property for relative symplectic cohomology |
| title_full_unstemmed | Mayer-Vietoris property for relative symplectic cohomology |
| title_short | Mayer-Vietoris property for relative symplectic cohomology |
| title_sort | mayer vietoris property for relative symplectic cohomology |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/117315 |
| work_keys_str_mv | AT varolgunesumut mayervietorispropertyforrelativesymplecticcohomology |