# Bundle Gerbes: Stable Isomorphism and Local Theory

@article{Murray1999BundleGS, title={Bundle Gerbes: Stable Isomorphism and Local Theory}, author={Michael K. Murray and Danny Stevenson}, journal={Journal of The London Mathematical Society-second Series}, year={1999}, volume={62}, pages={925-937} }

The notion of stable isomorphism of bundle gerbes is considered. It has the consequence that the stable isomorphism classes of bundle gerbes over a manifold M are in bijective correspondence with H 3 ( M , ℤ). Stable isomorphism sheds light on the local theory of bundle gerbes and enables a classifying theory for bundle gerbes to be developed using results of Gajer on B [Copf ] × bundles.

## 132 Citations

Reduction of strongly equivariant bundle gerbes with connection and curving

- Mathematics
- 2004

From a certain strongly equivariant bundle gerbe with connection and curving over a smooth manifold on which a Lie group acts, we construct under some conditions a bundle gerbe with connection and…

More morphisms between bundle gerbes.

- Mathematics
- 2007

Usually bundle gerbes are considered as objects of a 2-groupoid, whose 1- morphisms, called stable isomorphisms, are all invertible. I introduce new 1-morphisms which include stable isomorphisms,…

The Geometry of Bundle Gerbes

- Mathematics, Physics
- 2000

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…

Multiplicative bundle gerbes with connection

- Mathematics
- 2008

Abstract Multiplicative bundle gerbes are gerbes over a Lie group which are compatible with the group structure. In this article connections on such bundle gerbes are introduced and studied. It is…

Bundle gerbes on supermanifolds

- Mathematics
- 2020

We show that every bundle gerbe on a supermanifold decomposes into a bundle gerbe over the underlying manifold and a 2-form on the supermanifold. This decomposition is not canonical, but is…

On the splitting principle of bundle gerbe modules

- Mathematics
- 2007

We introduce the notion of an n-trivialization and a compatible curving and construct the splitting of bundle gerbe modules to define the twisted Chern classes and the twisted Chern character for…

The Canonical 2-Gerbe of a Holomorphic Vector Bundle

- Mathematics
- 2016

For each holomorphic vector bundle we construct a holomorphic bundle 2-gerbe that geometrically represents its second Beilinson-Chern class. Applied to the cotangent bundle, this may be regarded as a…

Bundle gerbes and the Weyl map

- Mathematics, Physics
- 2019

This masters thesis reviews bundle gerbe theory and the well-known basic bundle gerbe over SU(n). We introduce the cup product bundle gerbe, and show it is stably isomorphic to the pullback of the…

Yang-Mills theory for bundle gerbes

- Mathematics, Physics
- 2006

Given a bundle gerbe with connection on an oriented Riemannian manifold of dimension at least equal to 3, we formulate and study the associated Yang?Mills equations. When the Riemannian manifold is…

Gerbes and Lie Groups

- Mathematics, Physics
- 2011

Compact Lie groups do not only carry the structure of a Riemannian manifold, but also canonical families of bundle gerbes. We discuss the construction of these bundle gerbes and their relation to…

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