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https://hdl.handle.net/2440/615
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Type: | Journal article |
Title: | Bundle 2-gerbes |
Author: | Stevenson, D. |
Citation: | Proceedings of the London Mathematical Society, 2004; 88(2):405-435 |
Publisher: | London Math Soc |
Issue Date: | 2004 |
ISSN: | 0024-6115 1460-244X |
Abstract: | 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 \to 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. |
DOI: | 10.1112/S0024611503014357 |
Published version: | http://dx.doi.org/10.1112/s0024611503014357 |
Appears in Collections: | Applied Mathematics publications Aurora harvest |
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