Connections on Lie groupoids and Chern-Weil theory

Topological groupoids (including differentiable and Lie groupoids) (22A22) Pseudogroups and differentiable groupoids (58H05) Differential geometric aspects of gerbes and differential characters (53C08)

Cites Work

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Parallel transport on principal bundles over stacks
Lie crossed modules and gauge-invariant actions for 2-BF theories
The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module
Orbifolds as stacks?
Surface holonomy for non-Abelian 2-bundles via double groupoids
Differentiable stacks and gerbes
Chern-Weil map for principal bundles over groupoids
A groupoid approach to quantization
Non-abelian differentiable gerbes
Curvature and characteristic classes
Čech-De Rham theory for leaf spaces of foliations
Regular Cartan groupoids and longitudinal representations
Differential forms with values in VB-groupoids and its Morita invariance
Atiyah sequence and gauge transformations of a principal 2-bundle over a Lie groupoid
On two notions of a gerbe over a stack
Representations up to homotopy and Bott's spectral sequence for Lie groupoids
Atiyah sequences, connections and characteristic forms for principal bundles over groupoids and stacks
Deformation quantization of pseudo-symplectic (Poisson) groupoids
On the de Rham cohomology of differential and algebraic stacks
Secondary theories for étale groupoids
Twisted K-theory of differentiable stacks
On two-dimensional holonomy
Complex Analytic Connections in Fibre Bundles
Normal Forms and Lie Groupoid Theory
Higher lattices, discrete two-dimensional holonomy and topological phases in (3 + 1)D with higher gauge symmetry
Lie algebroids, gauge theories, and compatible geometrical structures
Atiyah sequences and connections on principal bundles over Lie groupoids and differentiable stacks

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