nonabelian de Rham cohomology

differential cohomology in an (∞,1)-topos -- survey
**structures in an (∞,1)-topos**
* **shape**
* **cohomology**
* cocycle/characteristic class
* twisted cohomology
* principal ∞-bundle
* ∞-vector bundle
* **homotopy**
* covering ∞-bundles
* Postnikov system
* path ∞-groupoid
* geometric realization
* Galois theory
* internal homotopy ∞-groupoid?
* Whitehead system
* **rational homotopy**
* ∞-Lie algebroid
* ordinary rational homotopy
* internal rational homotopy
* Chern-character
* **differential cohomology**
* flat differential cohomology
* de Rham cohomology
* de Rham theorem
* **relative theory over a base**
* relative homotopy theory
* Lie theory
## Examples
(...)
## Applications
* Background fields in twisted differential nonabelian cohomology
* Differential twisted String and Fivebrane structures
* D'Auria-Fre formulation of supergravity

In a ∞-connected (∞,1)-topos $\mathbf{H}$ a cocycle in *(nonabelian) de Rham cohomology* is a cocycle $\mathbf{\Pi}(X) \to A$ in flat differential cohomology whose underlying cocycle $X \hookrightarrow \mathbf{\Pi}(X) \to A$ in (nonabelian) cohomology is trivial: it encodes a trivial principal ∞-bundle with possibly nontrivial but *flat* connection.

Details are at

Revised on July 19, 2010 11:52:54
by Urs Schreiber
(131.211.36.96)