The notion of twisted -bundle is the generalization to higher geometry of the notion of twisted bundle.
Let be an (∞,1)-topos, an ∞-group, an object, and an ∞-representation of on , exhibited by a fiber sequence
which is identified with the universal -associated ∞-bundle.
Then for a -principal ∞-bundle, correspoding to a cocycle with coefficients in the moduli ∞-stack of -principal -bundles, the ∞-groupoid of sections of the associated ∞-bundle is equivalently the cocycle -groupoid of -twisted cohomology relative to :
Each such cocycle may be understood as locally having coefficients in , but globally being twisted by .
The geometric structure canonically associated to this is a (twisted -equivariant) -principal ∞-bundle on the total space of the twisting -bundle, seen by applying the pasting law of (∞,1)-pullbacks to the pasting diagram
Created on April 23, 2012 13:01:08
by Urs Schreiber