Exotic symplectic manifolds from Lefschetz fibrations

• Main Author: Maydanskiy, Maksim (Maksim Igorevich)
• Other Authors: Denis Auroux.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2010
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/50268

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 (p. 43-44). === 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. === by Maksim Maydanskiy. === Ph.D.