# Higher-Degree Analogs of the Determinant Line Bundle

- Authors
- Journal
- Communications in Mathematical Physics 0010-3616
- Publisher
- Springer-Verlag
- Publication Date
- Source
- Legacy
- Disciplines

## Abstract

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 subspace of the reduced K-theory of the parametrizing space, we construct a set of Deligne cohomology classes of degree i whose curvatures are the i -form component of the Atiyah-Singer families index theorem.

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