2001/06/04 by Danny Stevenson, Stevenson, Danny
Mathematics · #18D05 #55R65 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:18D05 #msc:55R65
paper · pdf · doi:10.48550/arxiv.math/0106018
27 pages
arxiv created 2001/06/04 · openalex publication_date 2001/06/04 · arxiv updated 2009/11/30 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
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.