Obstructions to the existence of displaceable Lagrangian submanifolds

Sirikci, Nil Ipek

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Description

Title

Obstructions to the existence of displaceable Lagrangian submanifolds

Author(s)

Sirikci, Nil Ipek

Issue Date

2012-06-27T21:24:11Z

Director of Research (if dissertation) or Advisor (if thesis)

Kerman, Ely

Doctoral Committee Chair(s)

Lerman, Eugene

Committee Member(s)

• Kerman, Ely
• Tolman, Susan
• Alexander, Stephanie B.

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Lagrangian submanifold
• Maslov index
• Conley-Zehnder index
• Floer theory
• Hamiltonian flows

Abstract

We utilize Floer theory and an index relation relating the Maslov index, Morse index and Conley-Zehnder index for a periodic orbit of the flow of a specific Hamiltonian function to state and prove some nonexistence results for certain displaceable Lagrangian submanifolds. We start with results under the assumption that the symplectic manifold (M,w) is closed and symplectically aspherical and then generalize to the case when (M,w) is weakly exact. The specific Lagrangian submanifolds in consideration are split hyperbolic submanifolds, spheres, products of spheres, Cayley projective plane and quaternionic projective spaces.

Graduation Semester

2012-05

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http://hdl.handle.net/2142/32007

Copyright and License Information

Copyright 2012 Nil Ipek Sirikci

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