Higher bundle gerbes and cohomology classes in gauge theories

Abstract

The notion of a higher bundle gerbe is introduced to give a geometric realization of the higher degree integral cohomology of certain manifolds. We consider examples using the infinite dimensional spaces arising in gauge theories.

16 pages, LaTeX

References in corpus (2)

• Index Theory, Gerbes, and Hamiltonian Quantization
• Mathematical remarks on the cohomology of gauge groups and anomalies

Cited by in corpus (22)

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• Classical Chern-Simons theory, Part 1
• The Geometry of Bundle Gerbes
• Dirac Charge Quantization and Generalized Differential Cohomology
• Tensor Berry connections and their topological invariants
• Leibniz 2-algebras and twisted Courant algebroids
• Discrete Torsion and Gerbes II
• Constructions with bundle gerbes
• Non-Abelian tensor Berry connections in multi-band topological systems
• The character map in (twisted differential) non-abelian cohomology
• The basic bundle gerbe on unitary groups
• Global gauge anomalies in two-dimensional bosonic sigma models
• Central extensions of gauge transformation groups of higher abelian gerbes
• Higher Gauge Theory and Integrability
• p-Gerbes and Extended Objects in String Theory
• Bundle gerbes and the Weyl map
• Equivariant smooth Deligne cohomology
• On the relationship of gerbes to the odd families index theorem
• Rigidified torsor cocycles, hypercoverings and bundle gerbes
• Current Groups and the Hamiltonian Anomaly
• Anomalies in gauge theory and gerbes over quotient stacks
• Flat principal 2-group bundles and flat string structures