Splitting the curvature of the determinant line bundle

Scott, Simon

doi:10.1090/S0002-9939-99-05311-3

Splitting the curvature of the determinant line bundle
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Proc. Amer. Math. Soc. 128 (2000), 2763-2775 Request permission

Abstract:

It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold $M=X^{0}\cup X^{1}$ has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from the families of Dirac operators over the two halves.

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