Bundle Gerbes: Stable Isomorphism and Local Theory

2000/12/01 by Michael K. Murray, Daniel Stevenson · 141 citations
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Bijection #Bundle #Chemistry #Clifford bundle #Combinatorics #Crystal structure #Crystallography #Frame bundle #Homotopy and Cohomology in Algebraic Topology #Isomorphism (crystallography) #Materials science #Mathematics #Normal bundle #Pure mathematics #Tautological line bundle #Vector bundle

paper · doi:10.1112/s0024610700001551

published in Journal of the London Mathematical Society 62(3), 925-937 (Wiley)

openalex publication_date 2000/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

The notion of stable isomorphism of bundle gerbes is considered. It has the consequence that the stable isomorphism classes of bundle gerbes over a manifold M are in bijective correspondence with H3(M, Z). Stable isomorphism sheds light on the local theory of bundle gerbes and enables a classifying theory for bundle gerbes to be developed using results of Gajer on BC× bundles.

Cited by

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• The basic bundle gerbe on unitary groups
• Basic gerbe over non-simply connected compact groups
• A bundle gerbe construction of a spinor bundle from the smooth free loop of a vector bundle
• WZW Orientifolds and Finite Group Cohomology
• Chern Character in Twisted K -Theory: Equivariant and Holomorphic Cases
• Categorical Structures on Bundle Gerbes and Higher Geometric Prequantisation
• MANY FINITE-DIMENSIONAL LIFTING BUNDLE GERBES ARE TORSION
• Sheaf theory for stacks in manifolds and twisted cohomology forS1–gerbes

Related

• Bundle gerbes: stable isomorphism and local theory
• An Introduction to Bundle Gerbes
• Reduction of strongly equivariant bundle gerbes with connection and curving
• The Geometry of Bundle Gerbes
• Constructions with bundle gerbes