TL;DR
This paper explores bundle gerbes as a geometric realization of three-dimensional integral cohomology, detailing their properties, connections, curvature, and relation to gerbes and Dixmier-Douady classes.
Contribution
It introduces bundle gerbes as an alternative geometric realization of third cohomology and discusses their key properties and connections.
Findings
Bundle gerbes provide a geometric realization of third cohomology.
Most known gerbes are examples of bundle gerbes.
Properties like connections and curvature are analyzed.
Abstract
Just as principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral cohomology through their Dixmier-Douady class. I consider an alternative, related, geometric realisation of three dimensional cohomology called a bundle gerbe. Every bundle gerbe gives rise to a gerbe and most of the well-known examples examples of gerbes are bundle gerbes. I discuss the properties of bundle gerbes, in particular bundle gerbe connections and curvature and their associated Dixmier-Douady class.
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Taxonomy
TopicsHistorical, Literary, and Cultural Studies