Splitting the Curvature of the Determinant Line Bundle

Details Splitting the Curvature of the Determinant Line Bundle Splitting the Curvature of the Determinant Line Bundle

1998-12-21

arxiv.org/abs/math/9812124v1

Mathematics

Analysis of PDEs

To appear in Proc. Am. Math. Soc

Scientific paper

It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold 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. This curvature form is the natural differential representative which satisifies the same splitting principle as the Chern class of the determinant line bundle.

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