## On nonabelian differential cohomology (2008)

### BibTeX

@MISC{Urs08onnonabelian,

author = {Urs},

title = {On nonabelian differential cohomology},

year = {2008}

}

### OpenURL

### Abstract

Nonabelian differential n-cocycles provide the data for an assignment of “quantities ” to n-dimensional “spaces ” which is • locally controlled by a given “typical quantity”; • globally compatible with all possible gluings of volumes. For n = 1 this encompasses the notion of parallel transport in fiber bundles with connection. In general we think of it as parallel n-transport. For low n and/or “sufficiently abelian quantities ” this has been modeled by differential characters, (n − 1)-gerbes, (n − 1)-bundle gerbes and n-bundles with connection. We give a general definition for all n in terms of descent data for transport n-functors along the lines of [7, 57, 58, 59]. Concrete realizations, notably Chern-Simons n-cocycles, are obtained by integrating L∞-algebras and their higher Cartan-Ehresmann connections [52]. Here we assume all gluing to happen through equivalences. If one