The Novikov theory for symplectic cohomology and exact Lagrangian embeddings
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465223198-MIT.pdf
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Full printable version
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606.29 KB
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Author(s)
Ritter, Alexander F. (Alexander Friedrich)
Advisor(s)
Paul Seidel.
Date Issued
2009
Publisher
Massachusetts Institute of Technology
Abstract
Given an exact symplectic manifold, can we find topological constraints to the existence of exact Lagrangian submanifolds? I developed an approach using symplectic cohomology which provides such conditions for exact Lagrangians inside cotangent bundles and inside ALE hyperkähler spaces. For example, the only exact Lagrangians inside ALE hyperkähler spaces must be spheres. The vanishing of symplectic cohomology is an obstruction to the existence of exact Lagrangians. In the above applications even though the ordinary symplectic cohomology does not vanish, one can prove that a Novikov homology analogue for symplectic cohomology does vanish.
Description
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 (leaves 121-123).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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