Higher-Degree Analogs of the Determinant Line Bundle

Details Higher-Degree Analogs of the Determinant Line Bundle Higher-Degree Analogs of the Determinant Line Bundle

2001-06-20

arxiv.org/abs/math/0106177v3

Mathematics

Differential Geometry

Final version

Scientific paper

10.1007/s00220-002-0686-3

In the first part of this paper, given a smooth family of Dirac-type operators on an odd-dimensional closed manifold, we construct an abelian gerbe-with-connection whose curvature is the three-form component of the Atiyah-Singer families index theorem. In the second part of the paper, given a smooth family of Dirac-type operators whose index lies in the i-th filtration of the reduced K-theory of the parametrizing space, we construct a set of Deligne cohomology class of degree i whose curvatures are the i-form component of the Atiyah-Singer families index theorem.

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