The Novikov theory for symplectic cohomology and exact Lagrangian embeddings
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2010
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| Online Access: | http://hdl.handle.net/1721.1/50271 |
| _version_ | 1826213172850196480 |
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| author | Ritter, Alexander F. (Alexander Friedrich) |
| author2 | Paul Seidel. |
| author_facet | Paul Seidel. Ritter, Alexander F. (Alexander Friedrich) |
| author_sort | Ritter, Alexander F. (Alexander Friedrich) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009. |
| first_indexed | 2024-09-23T15:44:30Z |
| format | Thesis |
| id | mit-1721.1/50271 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T15:44:30Z |
| publishDate | 2010 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/502712019-04-11T05:56:07Z The Novikov theory for symplectic cohomology and exact Lagrangian embeddings Ritter, Alexander F. (Alexander Friedrich) Paul Seidel. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Includes bibliographical references (leaves 121-123). Given an exact symplectic manifold, can we find topological constraints to the existence of exact Lagrangian submanifolds? I developed an approach using symplectic cohomology which provides such conditions for exact Lagrangians inside cotangent bundles and inside ALE hyperkähler spaces. For example, the only exact Lagrangians inside ALE hyperkähler spaces must be spheres. The vanishing of symplectic cohomology is an obstruction to the existence of exact Lagrangians. In the above applications even though the ordinary symplectic cohomology does not vanish, one can prove that a Novikov homology analogue for symplectic cohomology does vanish. by Alexander F. Ritter. Ph.D. 2010-01-07T15:49:50Z 2010-01-07T15:49:50Z 2009 2009 Thesis http://hdl.handle.net/1721.1/50271 465223198 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 123 leaves application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Ritter, Alexander F. (Alexander Friedrich) The Novikov theory for symplectic cohomology and exact Lagrangian embeddings |
| title | The Novikov theory for symplectic cohomology and exact Lagrangian embeddings |
| title_full | The Novikov theory for symplectic cohomology and exact Lagrangian embeddings |
| title_fullStr | The Novikov theory for symplectic cohomology and exact Lagrangian embeddings |
| title_full_unstemmed | The Novikov theory for symplectic cohomology and exact Lagrangian embeddings |
| title_short | The Novikov theory for symplectic cohomology and exact Lagrangian embeddings |
| title_sort | novikov theory for symplectic cohomology and exact lagrangian embeddings |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/50271 |
| work_keys_str_mv | AT ritteralexanderfalexanderfriedrich thenovikovtheoryforsymplecticcohomologyandexactlagrangianembeddings AT ritteralexanderfalexanderfriedrich novikovtheoryforsymplecticcohomologyandexactlagrangianembeddings |