Measures on differentiable stacks

Differentiable Stacks and Gerbes

We introduce differentiable stacks and explain the relationship with Lie groupoids. Then we study S-bundles and S-gerbes over differentiable stacks. In particular, we establish the relationship between S-gerbes and groupoid S-central extensions. We define connections and curvings for groupoid S-central extensions extending the corresponding notions of Brylinski, Hitchin and Murray for S-gerbes ...

Twisted K-theory of Differentiable Stacks

In this paper, we develop twisted K-theory for stacks, where the twisted class is given by an S-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure K α ⊗K j β → K i+j α+β are derived. Our approach provides a uniform framework for studying various twisted K-theories including the usual twisted K-theory of topological spaces...

S-Bundles and Gerbes over Differentiable Stacks

We study S-bundles and S-gerbes over differentiable stacks in terms of Lie groupoids, and construct Chern classes and Dixmier-Douady classes in terms of analogues of connections and curvature. c © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS S-Fibrés et Gerbes sur des Champs Différentiables Résumé. On étudie les S-fibrés et les S-gerbes sur des champs différentiab...

Notes on Differentiable Manifolds

On Differentiable Functionals