The Geometry of Bundle Gerbes

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 $H^4(M;\mathbb{Z})$ associated to any bundle 2-gerbe.

PhD thesis, 153 pages

References in corpus (4)

• Lectures on Special Lagrangian Submanifolds
• Geometry of Deligne cohomology
• Index Theory, Gerbes, and Hamiltonian Quantization
• Higher bundle gerbes and cohomology classes in gauge theories

Cited by in corpus (36)

• Twisted K-theory and K-theory of bundle gerbes
• An Invitation to Higher Gauge Theory
• Unoriented WZW Models and Holonomy of Bundle Gerbes
• More Morphisms between Bundle Gerbes
• Categorification and correlation functions in conformal field theory
• Constructions with bundle gerbes
• A Construction of String 2-Group Models using a Transgression-Regression Technique
• Connections on non-abelian Gerbes and their Holonomy
• From Loop Space Mechanics to Nonabelian Strings
• Four Equivalent Versions of Non-Abelian Gerbes
• Polyakov-Wiegmann Formula and Multiplicative Gerbes
• Transgressive loop group extensions
• Spherical T-Duality
• Division Algebras, Supersymmetry and Higher Gauge Theory
• Holonomy on D-Branes
• Multiplicative vector fields on bundle gerbes
• String Connections and Chern-Simons Theory
• Topological T-duality for torus bundles with monodromy
• The gauging of two-dimensional bosonic sigma models on world-sheets with defects
• Defects, dualities and the geometry of strings via gerbes. I. Dualities and state fusion through defects
• Gerbe-holonomy for surfaces with defect networks
• Relative Gerbes
• Basic equivariant gerbes on non-simply connected compact simple Lie groups
• Defects, dualities and the geometry of strings via gerbes II. Generalised geometries with a twist, the gauge anomaly and the gauge-symmetry defect
• Affine su(2) fusion rules from gerbe 2-isomorphisms
• Differential Geometry of Relative Gerbes
• Bundle gerbes on supermanifolds
• Differential Cocycles and Dixmier-Douady Bundles
• The ring structure for equivariant twisted K-theory
• Geometric and topological aspects of Type IIB D-branes
• A Coboundary Morphism For The Grothendieck Spectral Sequence
• Equivariant Cartan-Eilenberg supergerbes II. Equivariance in the super-Minkowskian setting
• Bundle gerbes and the Weyl map
• Anomalies in gauge theory and gerbes over quotient stacks
• Bicategories in field theories - an invitation
• The Dixmier-Douady class in the Simplicial de Rham Complex