The Index Gerbe

The Universal Gerbe and Local Family Index Theory

The goal of this paper is to apply the universal gerbe developed in [CMi1] and [CMi2] and the local family index theorems to give a unified viewpoint on the known examples of geometrically interesting gerbes, including the determinant bundle gerbes in [CMMi1], the index gerbe in [L] for a family of Dirac operators on odd dimensional closed manifolds. We also discuss the associated gerbes for a ...

On the Relationship of Gerbes to the Odd Families Index Theorem

The goal of this paper is to apply the universal gerbe of [CMi1] and [CMi2] to give an alternative, simple and more unified view of the relationship between index theory and gerbes. We discuss determinant bundle gerbes [CMMi1] and the index gerbe of [L] for the case of families of Dirac operators on odd dimensional closed manifolds. The method also works for a family of Dirac operators on odd d...

A Gerbe formulation of the Atiyah-Singer Index Theorem

Gerbes, Clifford Modules and the Index Theorem

The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators can be given natural interpretations using this language and that the resulting formula is still an identity.

The Geometry of Bundle Gerbes

This thesis reviews the theory of bundle gerbes and then examines the higher dimensional notion of a bundle 2-gerbe. The notion of a bundle 2-gerbe connection and 2-curving are introduced and it is shown that there is a class in H(M ;Z) associated to any bundle 2-gerbe.