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    • University of Missouri-Columbia
    • Graduate School - MU Theses and Dissertations (MU)
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    • 2006 Dissertations (MU)
    • 2006 MU dissertations - Freely available online
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    Complex and almost-complex structures on six dimensional manifolds

    Brown, James Ryan, 1977-
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    [PDF] research.pdf (308.5Kb)
    Date
    2006
    Format
    Thesis
    Metadata
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    Abstract
    We investigate the properties of hypothetical exotic complex structures on three dimensional complex projective space CP³. This is motivated by the long standing question in differential geometry of whether or not the six sphere S⁶ admits an integrable almost-complex structure. An affirmative answer to this question would imply the existence of many exotic complex structures on CP³. It is known that CP³ admits many topologically different almost-complex structures, but it is unknown whether or not CP³ admits an integrable almost-complex structure other that the standard Kaḧler structure. In this manuscript we give lower bounds on the Hodge numbers of hypothetical exotic structures on CP³ and a necessary condition for the Frol̈icher spectral sequence to degenerate at the second level. We also give topological constraints on the classes of hypothetical exotic complex structures which areC*-symmetric. We give restrictions on the fixed point sets of such C* actions.
    URI
    https://hdl.handle.net/10355/4466
    https://doi.org/10.32469/10355/4466
    Degree
    Ph. D.
    Thesis Department
    Mathematics (MU)
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    • 2006 MU dissertations - Freely available online
    • Mathematics electronic theses and dissertations (MU)

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