## 43 Citations

### Multiplicative Ehresmann connections

- Mathematics
- 2022

. We develop the theory of multiplicative Ehresmann connections for Lie groupoid submersions covering the identity, as well as their inﬁnitesimal counterparts. We construct obstructions to the…

### Connections on Lie groupoids and Chern-Weil theory

- Mathematics
- 2020

. Let X = [ X 1 ⇒ X 0 ] be a Lie groupoid equipped with a connection, given by a smooth distribution H ⊂ T X 1 transversal to the ﬁbers of the source map. Under the assumption that the distribution H…

### FOUR EQUIVALENT VERSIONS OF NONABELIAN GERBES

- Mathematics
- 2011

We recall and partially expand four versions of smooth, non-abelian gerbes: Cech cocycles, classifying maps, bundle gerbes, and principal 2-bundles. We prove that all these four versions are…

### A global perspective to connections on principal 2-bundles

- MathematicsForum Mathematicum
- 2018

For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action…

### Pontrjagin duality on multiplicative Gerbes.

- Mathematics
- 2020

We use Segal-Mitchison's cohomology of topological groups to define a convenient model for topological gerbes. We introduce multiplicative gerbes over topological groups in this setup and we define…

### ON 2-HOLONOMY

- MathematicsJournal of the Australian Mathematical Society
- 2019

Abstract We construct a cycle in higher Hochschild homology associated to the two-dimensional torus which represents 2-holonomy of a nonabelian gerbe in the same way as the ordinary holonomy of a…

## References

SHOWING 1-10 OF 53 REFERENCES

### Chern–Weil map for principal bundles over groupoids

- Mathematics
- 2004

The theory of principal G-bundles over a Lie groupoid is an important one unifying various types of principal G-bundles, including those over manifolds, those over orbifolds, as well as equivariant…

### Bundle gerbes

- Mathematics
- 1994

. Just as C × principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral…

### The basic gerbe over a compact simple Lie group

- Mathematics
- 2002

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 $H^3_G(G,\Z)$.…

### Sheaf theory for stacks in manifolds and twisted cohomology for S 1 -gerbes

- Mathematics
- 2007

In this paper we give a sheaf theory interpretation of the twisted cohomology of manifolds. To this end we develop a sheaf theory on smooth stacks. The derived push-forward of the constant sheaf with…

### Nonabelian Bundle Gerbes, Their Differential Geometry and Gauge Theory

- Physics
- 2005

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied…

### Deformation quantization modules I:Finiteness and duality

- Mathematics
- 2008

We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then we consider a $Z[\hbar]$-algebra satisfying…