The Geometry of Bundle Gerbes

TL;DR

This thesis explores the geometric theory of bundle gerbes and extends it to bundle 2-gerbes, introducing connections, 2-curvings, and their associated cohomology classes in a higher-dimensional setting.

Contribution

It provides a detailed review of bundle gerbes and introduces the concept of bundle 2-gerbes, including their connections, 2-curvings, and associated cohomology classes.

Findings

Defined bundle 2-gerbe connections and 2-curvings.

Established the association of a class in H^4(M;Z) to bundle 2-gerbes.

Extended the geometric framework of gerbes to higher dimensions.

Abstract

This thesis reviews the theory of bundle gerbes and then examines the higher dimensional notion of a bundle 2-gerbe. The notion of a bundle 2-gerbe connection and 2-curving are introduced and it is shown that there is a class in $H^{4}(M;\Z)$ associated to any bundle 2-gerbe.