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    Superconnections and index theory

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    kahlea.pdf (496.9Kb)
    Date
    2008-08
    Author
    Kahle, Alexander Rudolf
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    Abstract
    This document presents a systematic investigation of the geometric index theory of Dirac operators coupled superconnections. A local version of the index theorem for Dirac operators coupled to superconnection is proved, and extended to families. An [eta]-invariant is defined, and it is shown to satisfy an APS-like theorem. A geometric determinant line bundle with section, metric, and connection is associated to a family of Dirac operators coupled to superconnections, and its holonomy is calculated in terms of the [eta]-invariant.
    Department
    Mathematics
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    URI
    http://hdl.handle.net/2152/17871
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