Bundle gerbe

A Bündelgerbe is an object from algebraic topology, which was defined in 1995 by Michael K. Murray. It is a special type of Gerbe in the general sense, the special advantage is additional geometric structures - for example, a connection - to allow. These in turn make Bündelgerben with connection to an interesting part of the physics object.

The physical interest is based on the correspondence of Kategorifizierung on mathematical side and Stringifizierung on the physical side (both are not well-defined terms ): A gauge theory for point-like particles is described by a Hermitian line bundle with connection. Going to a string theory, so particles Hermitian line bundle with Hermitian connection by U (1) - Bündelgerben be strings, and replaced with context. In this case, in particular an abelian Bündelgerbe is interesting. But even non- Abelian Bündelgerben seem to find applications in M- theory.

Definition: A Hermitian U (1) - Bündelgerbe on a smooth manifold is a Hermitian line bundle together with and an isomorphism of Hermitian line bundles is a surjective submersion.

• Algebraic Topology