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Title:Obstructions to the existence of displaceable Lagrangian submanifolds
Author(s):Sirikci, Nil Ipek
Director of Research:Kerman, Ely
Doctoral Committee Chair(s):Lerman, Eugene
Doctoral Committee Member(s):Kerman, Ely; Tolman, Susan; Alexander, Stephanie B.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2012-06-27
URI:http://hdl.handle.net/2142/32007
Rights Information:Copyright 2012 Nil Ipek Sirikci
Date Available in IDEALS:2012-06-27
2014-06-28
Date Deposited:2012-05


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