David Michael Roberts

Yang-Mills theory for bundle gerbes

Given a bundle gerbe with connection on an oriented Riemannian manifold of dimension at least equal to 3, we formulate and study the associated Yang?Mills equations. When the Riemannian manifold is compact and oriented, we prove the existence of instanton solutions to the equations and also determine the moduli space of instantons, thus giving a complete analysis in this case. We also discuss duality in this context.

Equivariant bundle gerbes

We develop the theory of simplicial extensions for bundle gerbes and their characteristic classes with a view towards studying descent problems and equivariance for bundle gerbes. Equivariant bundle gerbes are important in the study of orbifold sigma models. We consider in detail two examples: the basic bundle gerbe on a unitary group and a string structure for a principal bundle. We show that the basic bundle gerbe is equivariant for the conjugation action and calculate its characteristic class; we show also that a string structure gives rise to a bundle gerbe which is equivariant for a natural action of the String 2-group.

On the existence of bibundles

We consider the existence of bibundles, in other words locally trivial principal

The Weak Choice Principle WISC may Fail in the Category of Sets

G

The Smooth Hom-Stack of an Orbifold

spaces with commuting left and right

On Certain 2-Categories Admitting Localisation by Bicategories of Fractions

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A topological fibrewise fundamental groupoid

actions. We show that their existence is closely related to the structure of the group

A bigroupoid’s topology (or, Topologising the homotopy bigroupoid of a space)

\Out(G)

The inner automorphism 3-group of a strict 2-group

of outer automorphisms of

Internal categories, anafunctors and localisations

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