The Geometry of Bundle Gerbes
Danny Stevenson (University of Adelaide)

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 associated to any bundle 2-gerbe.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Advanced Differential Geometry Research
