Symplectic cohomology of contractible surfaces
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2014
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| Online Access: | http://hdl.handle.net/1721.1/90184 |
| _version_ | 1826190313243279360 |
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| author | Jackson-Hanen, David Sean |
| author2 | Paul Seidel. |
| author_facet | Paul Seidel. Jackson-Hanen, David Sean |
| author_sort | Jackson-Hanen, David Sean |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014. |
| first_indexed | 2024-09-23T08:38:21Z |
| format | Thesis |
| id | mit-1721.1/90184 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T08:38:21Z |
| publishDate | 2014 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/901842019-04-09T18:54:32Z Symplectic cohomology of contractible surfaces Jackson-Hanen, David Sean 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, 2014. 27 Cataloged from PDF version of thesis. Includes bibliographical references (pages 55-56). In 2004, Seidel and Smith proved that the Liouville manifold associated to Ramanujams surface contains a Lagrangian torus which is not displaceable by Hamiltonian isotopy, and hence that higher products of this manifold provide non-standard symplectic structures on Euclidean space which are convex at infinity. I extend these techniques a wide class of smooth contractible affine surfaces of log-general type to produce a similar torus. I then show that the existence of this torus implies the non-vanishing of the symplectic cohomology of the Liouville manifolds associated to these surfaces, thus confirming a portion of McLeans conjecture that a smooth variety has vanishing symplectic cohomology if and only if it is affine ruled. by David Sean Jackson-Hanen. Ph. D. 2014-09-19T21:44:45Z 2014-09-19T21:44:45Z 2014 2014 Thesis http://hdl.handle.net/1721.1/90184 890211009 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 56 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Jackson-Hanen, David Sean Symplectic cohomology of contractible surfaces |
| title | Symplectic cohomology of contractible surfaces |
| title_full | Symplectic cohomology of contractible surfaces |
| title_fullStr | Symplectic cohomology of contractible surfaces |
| title_full_unstemmed | Symplectic cohomology of contractible surfaces |
| title_short | Symplectic cohomology of contractible surfaces |
| title_sort | symplectic cohomology of contractible surfaces |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/90184 |
| work_keys_str_mv | AT jacksonhanendavidsean symplecticcohomologyofcontractiblesurfaces |