More Morphisms between Bundle Gerbes

Abstract

Usually bundle gerbes are considered as objects of a 2-groupoid, whose 1-morphisms, called stable isomorphisms, are all invertible. I introduce new 1-morphisms which include stable isomorphisms, trivializations and bundle gerbe modules. They fit into the structure of a 2-category of bundle gerbes, and lead to natural definitions of surface holonomy for closed surfaces, surfaces with boundary, and unoriented closed surfaces.

40 pages

References in corpus (8)

• Twisted K-theory and K-theory of bundle gerbes
• WZW branes and gerbes
• TFT construction of RCFT correlators II: Unoriented world sheets
• The Geometry of Bundle Gerbes
• Unoriented WZW Models and Holonomy of Bundle Gerbes
• Abelian and non-Abelian branes in WZW models and gerbes
• Basic gerbe over non simply connected compact groups
• Categorification and correlation functions in conformal field theory

Cited by in corpus (27)

• Bi-branes: Target Space Geometry for World Sheet topological Defects
• A Construction of String 2-Group Models using a Transgression-Regression Technique
• Bundle Gerbes and Surface Holonomy
• Connections on non-abelian Gerbes and their Holonomy
• Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
• Spin structures on loop spaces that characterize string manifolds
• Geometry and 2-Hilbert Space for Nonassociative Magnetic Translations
• Four Equivalent Versions of Non-Abelian Gerbes
• String geometry vs. spin geometry on loop spaces
• Fluxes, bundle gerbes and 2-Hilbert spaces
• Transgressive loop group extensions
• String Connections and Chern-Simons Theory
• Smooth Functorial Field Theories from B-Fields and D-Branes
• The gauging of two-dimensional bosonic sigma models on world-sheets with defects
• Quantization of Magnetic Poisson Structures
• Defects, dualities and the geometry of strings via gerbes. I. Dualities and state fusion through defects
• Affine su(2) fusion rules from gerbe 2-isomorphisms
• Defects, dualities and the geometry of strings via gerbes II. Generalised geometries with a twist, the gauge anomaly and the gauge-symmetry defect
• Twisted K-theory and obstructions against positive scalar curvature metrics
• Bundle gerbes on supermanifolds
• Differential Cocycles and Dixmier-Douady Bundles
• Smooth Fock bundles, and spinor bundles on loop space
• Bigerbes
• Topological Insulators and the Kane-Mele Invariant: Obstruction and Localisation Theory
• Gerbes in Geometry, Field Theory, and Quantisation
• Current Groups and the Hamiltonian Anomaly
• Bicategories in field theories - an invitation