Superconnections and Index Theory

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Kahle, Alexander
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Abstract
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We investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate eta-invariants and prove an APS-theorem, and construct a geometric determinant line bundle for families of such operators, computing its curvature and holonomy in terms of familiar index theoretic quantities.
Comment: 29 pages, 1 figure; minor updates and corrections; final version
Keywords
Mathematics - Differential Geometry, Mathematics - K-Theory and Homology
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