Differential geometry of gerbes

Differential Geometry of Gerbes and Differential Forms

We discuss certain aspects of the combinatorial approach to the differential geometry of non-abelian gerbes due to W. Messing and the author [5], and give a more direct derivation of the associated cocycle equations. This leads us to a more restrictive definition than in [5] of the corresponding coboundary relations. We also show that the diagrammatic proofs of certain local curving and curvatu...

Differential Geometry of Gerbes Lawrence Breen and William Messing

0. Introduction 1 1. Torsors and associated gauge groups 5 2. Gerbes and their gauge stacks 7 3. Morita theory 12 4. The gauge stack as an inner form 13 5. Comparison with the explicit cocycles 20 6. Connections on torsors and groups 23 7. Connections on gerbes 32 8. Curving data and the higher Bianchi identity 40 9. Partially decomposed gerbes with connections 48 10. Fully decomposed gerbes wi...

The Geometry of Bundle Gerbes

This thesis reviews the theory of bundle gerbes and then examines the higher dimensional notion of a bundle 2-gerbe. The notion of a bundle 2-gerbe connection and 2-curving are introduced and it is shown that there is a class in H(M ;Z) associated to any bundle 2-gerbe.

Recurrent metrics in the geometry of second order differential equations

Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...

Geometry II - Discrete Differential Geometry