# 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}, year={1999}, volume={62} }

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 H3(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 BC× bundles.

## 131 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…

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…

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…

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,…

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
- 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…

Nonabelian Bundle Gerbes, Their Differential Geometry and Gauge Theory

- Physics
- 2005

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied…

Yang-Mills theory for bundle gerbes

- Mathematics
- 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…

## References

SHOWING 1-10 OF 22 REFERENCES

Bundle gerbes

- Mathematics
- 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…

Curvature and Characteristic Classes

- Mathematics
- 1978

Differential forms and cohomology.- Multiplicativity. The simplicial de rham complex.- Connections in principal bundles.- The chern-weil homomorphism.- Topological bundles and classifying spaces.-…

Geometry of Deligne cohomology

- Mathematics
- 1997

It is well known that degree two Deligne cohomology groups can be identified with groups of isomorphism classes of holomorphic line bundles with connections. There is also a geometric description of…

Principal Bundles and the Dixmier Douady Class

- Mathematics
- 1998

Abstract:A systematic consideration of the problem of the reduction and “lifting” of the structure group of a principal bundle is made and a variety of techniques in each case are explored and…

Index Theory, Gerbes, and Hamiltonian Quantization

- Physics
- 1997

Abstract: We give an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and prove that this leads in a…

Lectures on Special Lagrangian Submanifolds

- Mathematics
- 1999

These notes consist of a study of special Lagrangian submanifolds of Calabi-Yau manifolds and their moduli spaces. The particular case of three dimensions, important in string theory, allows us to…

Loop Spaces, Characteristic Classes and Geometric Quantization

- Mathematics
- 1994

This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Recent developments in mathematical…

Algebraic Topology

- Mathematics

The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.

On C*-Diagonals

- MathematicsCanadian Journal of Mathematics
- 1986

Preface. The impetus for this study arose from the belief that the structure of a C*-algebra is illuminated by an understanding of the manner in which abelian subalgebras embed in it. Posed in its…

Gerbes and massive type II configurations

- Physics
- 1999

We find novel bound states of NS5, D6 and D8-branes in massive type IIA string theory. As the NS gauge transformations can change the Chern class of the RR field these configurations should be…