2026-09-19T21:37:19Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/901842026-06-16T18:52:37Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Paul Seidel.
Jackson-Hanen, David Sean
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2014-09-19T21:44:45Z
2014-09-19T21:44:45Z
2014
2014
http://hdl.handle.net/1721.1/90184
890211009
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.
56 pages
eng
Massachusetts Institute of Technology
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
Mathematics.
Symplectic cohomology of contractible surfaces
Thesis
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