differential cohomology in an (∞,1)-topos – survey
internal homotopy ∞-groupoid?
(…)
Background fields in twisted differential nonabelian cohomology?
In a locally contractible (∞,1)-topos $\mathbf{H}$ with internal path ∞-groupoid functor $(\mathbf{\Pi} \dashv \mathbf{\flat})$, the flat differential cohomology of an object $X$ with coefficient in an object $A$ is the $A$-cohomology of the path ∞-groupoid $\mathbf{\Pi}(X)$:
The constant path inclusion $X \to \mathbf{\Pi}(X)$ induces a morphism
which sends a flat differential cocycle to its underlying or bare cocycle.
The obstruction theory for lifts through this morphism is the differential cohomology of $X$.
See differential cohomology in an (∞,1)-topos for more details.
Last revised on May 29, 2012 at 22:04:00. See the history of this page for a list of all contributions to it.