Symplectic cohomology of contractible surfaces

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2014

Author dc:creator

• Jackson-Hanen, David Sean

Advisor dc:contributor.advisor

• Paul Seidel.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/90184

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/90184