Bundle gerbes and the Weyl map

TL;DR

This thesis explores bundle gerbe theory, introducing the cup product bundle gerbe and demonstrating its stable isomorphism to the pullback of the basic bundle gerbe over SU(n) via the Weyl map, enriching understanding of their applications.

Contribution

It introduces the cup product bundle gerbe and proves its stable isomorphism to the pullback of the basic bundle gerbe via the Weyl map, advancing bundle gerbe theory.

Findings

The cup product bundle gerbe is stably isomorphic to the pullback of the basic bundle gerbe by the Weyl map.

Enhanced understanding of the basic bundle gerbe's structure and applications.

Provides a new perspective on bundle gerbe constructions over SU(n).

Abstract

This masters thesis reviews bundle gerbe theory and the well-known basic bundle gerbe over SU(n). We introduce the cup product bundle gerbe, and show it is stably isomorphic to the pullback of the basic bundle gerbe by the Weyl map. This result enriches our understanding of the basic bundle gerbe, which has numerous applications in physics.