The basic gerbe over a compact simple Lie group

TL;DR

This paper constructs an equivariant gerbe with connection on a compact, simply connected simple Lie group, representing a generator of the equivariant third cohomology group, and develops related technical tools.

Contribution

It introduces a new construction of equivariant gerbes with connection on Lie groups and develops a gluing method and theory for equivariant bundle gerbes.

Findings

Constructed an equivariant gerbe with connection on G

Represented a generator of H^3_G(G,Z) with equivariant 3-curvature

Developed a gluing construction and theory for equivariant bundle gerbes

Abstract

Let $G$ be a compact, simply connected simple Lie group. We give a construction of an equivariant gerbe with connection on $G$, with equivariant 3-curvature representing a generator of $H^3_G(G,\Z)$. Technical tools developed in this context include a gluing construction for gerbes and a theory of equivariant bundle gerbes.