Premium
Bundle 2‐gerbes
Author(s) -
Stevenson Daniel
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611503014357
Subject(s) - mathematics , bundle , connection (principal bundle) , principal bundle , pure mathematics , morphism , frame bundle , characteristic class , class (philosophy) , normal bundle , tautological line bundle , vector bundle , cohomology , geometry , computer science , artificial intelligence , materials science , composite material
We make the category BGrb M of bundle gerbes on a manifold M into a 2‐category by providing 2‐cells in the form of transformations of bundle gerbe morphisms. This description of BGrb M as a 2‐category is used to define the notion of a bundle 2 ‐gerbe. To every bundle 2‐gerbe on M is associated a class in H 4 ( M ; Z). We define the notion of a bundle 2‐gerbe connection and show how this leads to a closed, integral, differential 4‐form on M which represents the image in real cohomology of the class in H 4 ( M ; Z}. Some examples of bundle 2‐gerbes are discussed, including the bundle 2‐gerbe associated to a principal G bundle P → M . It is shown that the class in H 4 ( M ; Z} associated to this bundle 2‐gerbe coincides with the first Pontryagin class of P : this example was previously considered from the point of view of 2‐gerbes by Brylinski and McLaughlin. 2000 Mathematics Subject Classification 18D05, 55R65.