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    Lagrangian bubmanifolds of products of spheres

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    Date
    2014-08
    Author
    Oakley, Joel Stantford
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    Abstract
    This work investigates certain Lagrangian submanifolds of products of spheres. In particular, we will study several constructions of "exotic" Lagrangian tori in S^2 x S^2, and we will prove that they are all Hamiltonian isotopic. In the space (S^2)^3, we will investigate a Lagrangian submanifold that is diffeomorphic to RP^3, and we will prove that it is nondisplaceable under Hamiltonian diffeomorphisms by showing that the homology of a certain chain complex (called the pearl complex) is non-trivial.
    URI
    http://purl.galileo.usg.edu/uga_etd/oakley_joel_s_201408_phd
    http://hdl.handle.net/10724/31257
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    • University of Georgia Theses and Dissertations

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