Bundle 2-gerbes

Stevenson, D. (2004) Bundle 2-gerbes. Proceedings of the London Mathematical Society, 88(2), pp. 405-435. (doi: 10.1112/S0024611503014357)

Abstract

We make the category BGrbM 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 BGrbM 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 H4(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 H4(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 H4(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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Stevenson, Dr Daniel
• Authors: Stevenson, D.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the London Mathematical Society
• Journal Abbr.: Proc. London Math. Soc.
• ISSN: 0024-6115
• ISSN (Online): 1460-244X