# Bundle gerbes

@inproceedings{Murray1994BundleG, title={Bundle gerbes}, author={Michael K. Murray}, year={1994} }

. Just as C × principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral cohomology through their Dixmier-Douady class. I consider an alternative, related, geometric realisation of three dimensional cohomology called a bundle gerbe. Every bundle gerbe gives rise to a gerbe and most of the well-known examples examples of gerbes are bundle gerbes. I discuss the properties…

## 314 Citations

### Equivariant bundle gerbes

- Mathematics
- 2015

We develop the theory of simplicial extensions for bundle gerbes and their characteristic classes with a view towards studying descent problems and equivariance for bundle gerbes. Equivariant bundle…

### Gerbes in Geometry, Field Theory, and Quantisation

- MathematicsComplex Manifolds
- 2021

Abstract This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes…

### 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…

### Crossed module bundle gerbes; classification, string group and differential geometry

- Mathematics
- 2011

We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to a (Lie) crossed module (H → D) there is a simplicial group , the nerve of the groupoid…

### Gerbes and Lie Groups

- Mathematics
- 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…

### 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…

### The Geometry of Bundle Gerbes

- Mathematics
- 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…

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