Exotic symplectic manifolds from Lefschetz fibrations

In this thesis I construct, in all odd complex dimensions, pairs of Liouville domains W0 and W1 which are diffeomorphic to the cotangent bundle of the sphere with one extra subcritical handle, but are not symplectomorphic. While W0 is symplectically very similar to the cotangent bundle itself, W1 is more unusual. I use Seidel's exact triangles for Floer cohomology to show that the wrapped Fukaya category of W1 is trivial. As a corollary we obtain that W1 contains no compact exact Lagrangian submanifolds.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2009

Author dc:creator

• Maydanskiy, Maksim (Maksim Igorevich)

Advisor dc:contributor.advisor

• Denis Auroux.

• 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/1721.1/50268

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/50268